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Homework Assignments

Spring 2004

• Assignment #1
  • Log on to my home page, follow the link to the syllabus, then read the syllabus. In the syllabus, you will find directions for using the WebBoard. Once you have completed reading the syllabus, log onto the WebBoard and respond to the welcome message on the WebBoard, saying something like "I've read the syllabus and am ready for a great semester."
• Assignment #2
  • During the first class meeting, I will pass out information sheets. These sheets will ask for information that will assist me in providing you with as much help as possible. Fill in the questions asked on the sheet, then visit me in my office (bring the sheet with you) before the first week of classes are over.
• Assignment #3
  • Read Section 1.1, pages 2-8.
  • For exercises #61, 62, and 63 on page 10, list variables and what they represent, then set up an expression using those variables that satisfies the problem statement.
  • For exercises #63, 64, 66, and 67 on pages 10-11, copy the figure given onto your homework paper, then find the solution to each exercise, arranging your work in an orderly fashion, using complete sentences to describe what you are doing at each step.
  • For exercises #68, 69, 70, and 71, copy the given expression onto your homework paper, the substitute the given values and simplify the expression. Connect each step to the preceding step with an equal sign and align your equal signs in a vertical column as you proceed with your solution.
  • For exercises #72, 73, and 74 on page 11, copy down the given expression, then answer the question with a complete sentence (subject, verb, punctuation, etc.)
• Assignment #4
  • Read Section 1.2, pages 11-18.
  • On page 19, do exercises #7, 8, 11, and 14. Arrange your work as shown in Example 3 on page 12, connecting each succesive step to the one that precedes it with an equal sign. You may, if you wish, sketch a factor tree off to the side of this computation.
  • On page 19, do exercises #17, 18, 24, and 27, arranging your work as shown in Examples 7 and 8, connecting each successive step to the preceding step with an equal sign. Please work vertically, aligning equal signs in a column as your work, as shown in Examples 7 and 8.
  • On page 19, do exercises # 41, 42, 49, and 54, arranging your work as shown in Example 10a, connecting each successive step to the preceding step with an equal sign. Please work vertically, aligning equal signs in a column as your work.
  • On page 20, do exercises #73, 74, and 75. First, copy the given image onto your homework paper. Secondly, find the the requested quantity, arranging your work as in preceding exercises.
• Assignment #5
  • Read Section 1.3, pages 20-27.
  • On page 27, do exercises #17 and 22, arranging your work as shown in Examples 3 and 4.
  • On page 27, write the given statement in exercises #38 and 39 with the correct inequality symbol.
  • On Page 28, do exercises #55 and 56. First copy down the given problem, then evaluate, connecting your answer to the given problem with an equals sign.
  • On page 28, answer exercises #59-63 with a complete sentence (subject, verb, punctuation, etc.).
  • On page 28, do exercises #75 and 76. In each exercise, express each of the fractions with a common denominator, then list them in order, from least to greatest.
• Assignment #6
  • Read Section 1.4, pages 28-32.
  • On page 32, do exercises #1 and 8. In each case, draw a number line, then show the addition as in Examples 1, 2, 3, and 4.
  • On page 32, do exercises #9, 16, 19, 32, 33, 39, 42. Arrange your work as shown in Example 5, parts a-e. However, if your solution requires more than one step, please work vertically, arranging your equal signs in a column as your work.
• Assignment #7
  • Read Section 1.5, pages 34-38.
  • On page 38, do exercises #22, 23, 26, 41, 63, 66, 67, 85, and 86. In each case, arrange your work by first copying down the original problem, then proceeding as shown in Example 8. If the problem requires more than one step, please work vertically, arranging your equal signs in a column as you work.
• Assignment #8
  • Read Section 1.6, pages 40-45.
  • On pages 45-46, do exercises #1, 10, 13, 14, 19, 24, 33, 34, 93, 96, 97. In each case, copy the original problem onto your homework paper, then arrange your work as shown in Example 7a. If the problem requires more than one step, please work vertically, arranging your equal signs in a column as you work.
• Assignment #9
  • Read Section 1.7, pages 47-53.
  • On page 53, use the distributive property to multiply in exercises # Page 53, $33, 38, 39, and 42. Begin by copying the original problem onto your homework paper, then arranging your work as shown in Examples 6, 7, and 8.
  • On page 53, use the distributive property to factor the given expressions in exercises #47, 52, 57, and 60, arranging your work as shown in Example 9.
  • On pages 53-54, do exercises #71, 74, 79, and 80, arranging your work as shown in Example11. Copy the original problem, the connect successive steps to the previous step with an equal sign. If the problem requires more than one step, please work vertically, aligning your equal signs in a column as your work.
  • On page 54, copy the figure in exercise #83 onto your homework paper, then use a complete sentence (subject, verb, punctuation, etc.) to state the perimeter of the figure.
• Assignment #10
  • Read section 1.8, pages 55-62.
  • For each of the following exercises, begin by copying the problem exactly onto your homework paper. Then simplify, following the format shown in example 2c and example 7 in the text. Try to align the equal signs in a column, as demonstrated in Example 7. Page 62, #17, 18, 25, 26, 31, 32, 49.
  • For each of the following exercises, begin by copying the problem exactly onto your homework paper. Then use your calculator to find a decimal approximation for exercises #57-60 on page 63. It is not required to show any work. Simply copy down the problem, find the approximation with your calculator, and attach it to the problem with an equals sign.
  • For each of the following exercises, begin by copying the problem exactly onto your homework paper. Then use your calculator, as shown in example 8, to find an approximation. Attach this approximation to the problem with an equals sign. Page 63, #68, 72, 74.
  • For each of the following exercises, begin by copying the problem exactly onto your homework paper. Then simplify, following the format shown in examples 12 and/or 14 in the text. Try to align the equal signs in a column as demonstrated in these examples. Page 62, #81, 86, 89, 92, 98, 99,
• Assignment #11
  • Read section 2.1, pages 70-76.
  • For each of the following exercises, begin by copying the problem exactly onto your homework paper. Then, find the solution, showing all appropriate steps along the way. If you do not show the steps in the process, you will receive no credit for your solution. Please arrange your work so that the equal signs in each step are aligned in a column. Page 76, #3, 7, 11, 15, 19, 21, 23, 25, 29, 35, 37, 39, 41, 43, 47.
  • Although you should always check each and every solution, it is only required that you show the check for each of the following questions above: #15, 21, 37, and 47.
• Assignment #12
  • Read section 2.2, pages 77-82.
  • For each of the following exercises, begin by copying the problem exactly onto your homework paper. Then, find the solution, showing all appropriate steps along the way. If you do not show the steps in the process, you will receive no credit for your solution. Please arrange your work so that the equal signs in each step are aligned in a column. Page 83, #1, 9, 19, 21, 25, 27, 33, 37, 37, 41, 43, 47, 51, 55, 59, 61, 63, 67.
  • Although you should always check each and every solution, it is only required that you show the check for each of the following questions above: #9, 25, 47, and 55. Use your calculator to check the remaining problems as demonstrated in Examples 2, 4, 5, and 8 in the text, but these are not required to be turned it.
• Assignment #13
  • In Bittinger, read Section 2.3, pages 85-89.
  • Use the technique demonstrated in Example 2 to answer exercise #7 on page 90.
  • Page 90-92, do exercises #11, 13, 17, 19, 21, 27, 31, 33, 38, 39, 40, and 50. In each case, copy the problem down and show each step of the solution process, taking care to align your equal signs in a column at each step.
• Assignment #14
  • In Bittinger, read Section 2.4, pages 92-97.
  • For exercises #1, 7, 11, 15, 19, 21, 25, 29, 33, 35, 37, 39, 41, 43, 45, 47, 49, 53, 55, 57, 63, and 65 on pages 97-99, perform each of the following tasks.
    1. Make a list of the variable(s) used in your solution and state what each represents.
    2. Gather and organize the given data in each exercise. If the problem involves geometry, draw and label a figure. Use charts and/or tables to summarize the given data in other situations.
    3. Set up an equation that models the problem statement.
    4. Solve the equation.
    5. Write a sentence or two that answers the question posed in the problem. Look Back. Does your answer makes sense? Note: This means more than simply checking the solution to your equation in the original equation setup to model the problem statement. Rather, go back to the original problem statement and check to see if the solution you have found satisfies the constraints posed in the problem.
• Assignment #15
  • In Bittinger, read Section 2.5, pages 99-107.
  • For each of the following exercises, perform each of the following tasks.
    1. Make a list of the variable(s) used in your solution and state what each represents.
    2. Gather and organize the given data in each exercise. If the problem involves geometry, draw and label a figure. Use charts and/or data to summarize the given data in other situations.
    3. Set up an equation that models the problem statement.
    4. Solve the equation.
    5. Write a sentence or two that answers the question posed in the problem. Look Back. Does your answer makes sense? Note: This means more than simply checking the solution to your equation in the original equation setup to model the problem statement. Rather, manually check to see if the solution you have found satisfies the constraints posed in the problem.
    Pages 107-110, Exercises #1, 7, 11, 13, 17, 23, 35, 31, 33, 49, 51, 56, and 58.
• Assignment #16
  • In Bittinger, read Section 2.6, pages 110-118.
  • For each of the following exercises, sketch the solution set on a number line. Page 119, #5, 7.
  • For each of the following exercises, sketch the number line solution given in the exercise, then describe the solution set using both set-builder and interval notation. Page 119, #15, 17, 20, and 22.
  • For each of the following exercises, solve the given inequality, then sketch the solution on a number line. Describe the solution set using both set-builder and interval notation. Page 119, #23, 31, 51, 53, 59, 65, 69, 73, 77, 78, 80, 83, 85, and 99.
• Assignment #17
  • In Bittinger, read Section 3.1, pages 134-141.
  • In Bittinger, read Section 3.2, pages 145-151.
  • Fact: The graph of an equation having the form y = mx + b is a line. If we know ahead of time that the graph is a line, then we need only find two points that satisfy the equation of the line, plot them, then draw a line through the two points. In Bittinger, for exercises #21, 23, and 25 on page 152 of Bittinger, perform each of the following tasks.
    1. Using hand calculations only, set up a table of two points that satisfy the given equation. Please place this table on your graph paper near the plot of the given equation.
    2. On a sheet of graph paper, set up and scale coordinate axes, plot the two points from your table, then draw a line through the plotted points. Label your line with its equation.
    3. Compare the equation with the form y = mx + b, then indicate the values of m and b on your plot.
    4. Use your graphing calculator to draw the graph of the given equation, then compare with your hand plot.
  • For exercises #31, 33, 35, 37, and 39 on page 152 of Bittinger, perform each of the following steps.
    1. Using hand calculations only, set up a table of points that satisfy the given equation. Use these x-values: -3, -2, -1, 0, 1, 2, and 3. Please place this table on your graph paper near your plot of the given equation.
    2. Use the table feature of your calculator to check your hand calculated tabular results.
    3. On a sheet of graph paper, set up and scale coordinate axes, then plot the points in your table on your coordinate system. Sketch the remainder of the points that satisfy the equation. Use a ruler where you determine the graph will be linear, but draw a smooth freehand curve through the plotted tabular points where the graph appears to be nonlinear (some sort of curve). Label the resulting graph with its equation. Check the plot with your graphing calculator.
  • In Bittinger, page 152, exercises #41, 43, 45, and 46, use your graphing calculator to plot the graph of the equation in each of the given viewing windows. Copy the result from your viewscreen to your homework paper, label the x- and y-axes, then place the Window parameters Xmin, Xmax, Ymin, and Ymax on your axes. Please do a separate plot for each viewing window.
  • In Bittinger, page 153, exercise #71, use your graphing calculator to draw the graph of the given equation. Follow the given instructions in the exercise, then copy the plot in your viewscreen onto your homework paper as best you can. Be sure to include your Window parameters Xmin, Xmax, Ymin, and Ymax on your plot.
• Assignment #18
  • In Bittinger, read Section 3.3, pages 154-161.
  • In Bittinger, page 162, exercises #9, 11, 13, and 17, perform each of the following tasks.
    1. On a sheet of graph paper, graph each side of the equation. Label and scale each axis. Label each graph with its equation.
    2. Draw a number line below your graph and drop a dashed, vertical line from the point of intersection to your number line. Shade and label the x-value of the point of intersection on your number line.
    3. Solve the equation analytically (algebraically). Make sure you answer compares to that found in part (2) before proceeding to the next exercise.
  • In Bittinger, page 162, exercises #25 and 27, peform each of the following tasks.
    1. Enter each side of the given equation into the Y= menu on your calculator. Adjust the viewing window so that the point of intersection is visible. When you are satisfied, make a copy of your viewing window on your homework paper. Label your axes, then indicate the values of xmin, xmax, ymin, and ymax on your axes.
    2. Use the intersect utility on your CALC menu to find the point of intersection of the two graphs. Draw a number line below your plot on your homework. Drop a dashed, vertical line from the point of intersection to the number line and shade and label the x-value of the point of intersection on your number line.
    3. Solve the exercise analytically (algebraically). Make sure that your answer compares favorably to that found in part (2) before proceeding to the next exercise.
  • In Bittinger, page 164, exercises #63, 65, and 67, perform each of the following tasks.
    1. Enter each side of the given equation into the Y= menu on your calculator. Adjust the viewing window so that the point of intersection is visible. When you are satisfied, make a copy of your viewing window on your homework paper. Label your axes, then indicate the values of xmin, xmax, ymin, and ymax on your axes.
    2. Use the intersect utility on your CALC menu to find the point(s) of intersection of the two graphs. Draw a number line below your plot on your homework. Drop a dashed, vertical line(s) from the point(s) of intersection to the number line and shade and label the x-value(s) of the point(s) of intersection on your number line.
• Assignment #19
  • In Bittinger, read Section 3.3, pages 160-161.
  • In Bittinger, page 163, duplicate the graphs in exercises #41 and 42 on a sheet of graph paper. Draw a number line below the graph, then drop a dashed, vertical line from the point of intersection of the two lines. Shade the solution of the inequality on your number line below your plot, then use both set-builder and interval notation to describe the solution set.
  • In Bittinger, page 163, in exercises #48, 50, and 51, perform each of the following tasks.
    1. Sketch the graph of each side of the inequality on the same set of coordinate axes on a sheet of graph paper. Draw a number line below your plot, then drop a dashed, vertical line from the point of intersection of the two lines to your number line. Shade the solution of the inequality on the number line, then use both set-builder and interval notation to describe your solution.
    2. Solve the inequality algebraically and sketch the solution set on a number line. Make sure that this solution compares favorably with that found in part (1) before attempting the next exercise.
  • In Bittinger, page 163, in exercises #52, 53, and 54, perform each of the following tasks.
    1. Use your graphing calculator to sketch each side of the inequality. Place the left-hand side of the inequality in Y1, the right in Y2. Adjust the Window parameters until all points of intersection are visible in your viewing window.
    2. Make a copy of your viewing window on your homework paper. Label each axis and scale each axis with the Window parametersn xmin, xmax, ymin, and ymax.
    3. Use the intersect utility in the CALC menu to find the x-value of each point of intersection.
    4. Draw a number line below your sketch. Drop dashed, vertical lines from the point(s) of intersection to your number line. Shade the solution of the given inequality on your number line, then use both set-builder and interval notation to describe the solution set.
    5. Solve the inequality algebraically and shade the solution on a number line. Make sure that your solution compares favorably with that found in part (4) before attempting the next exercise.
  • In Bittinger, page 164, in exercises #69, 71, and 73, follows the directions, parts (1)-(4) only, from the previous exercise.
• Assignment #20
  • In Bittinger, read Section 3.4, pages 164-172.
  • In Bittinger, page 172, exercise #1. On a sheet of graph paper, plot the given data and draw a "line of best fit" through the data. Be sure to label and indicate the scale on each axis.
  • In Bittinger, page 172, exercise #3, perform the following tasks.
    1. On a sheet of graph paper, plot the given data. Be sure to label and indicate the scale on each axis. Connect the points with a straightedge to create a so-called "line graph." Note: A line graph is different from a "line of best fit." Be sure to read about the difference in your text.
    2. Enter the data into the graphing calculator, then draw a line plot. Copy the plot in the viewing window onto your homework paper. Be sure that it compares favorably with that drawn in part (1) before continuing to the next exercise.
  • In Bittinger, page 173, exercise #9, 10, perform each of the following tasks.
    1. Enter the equation into Y1 in your calculator, then enter 80 into Y2. Adjust the Window parameters until the points of intersection are visible in the viewing window, then use the intersect utility to find the x-values of these points of intersection. Copy the graph onto your homework paper, drop dashed, vertical lines from the points of intersection to a number line below your graph, then label these points on your number line. What years do these points represent?
    2. For exercise #10, use the value utility in the CALC menu to determine the number of refunds in 1996. Label this point in your sketch in part (1).
  • In Bittinger, page 174, solve each of the following exercises using graph paper. Exercises #13, 18, 19, and 20.
  • In Bittinger, pages 174-175, solve each of the following using a graphing calculator. Set up the model, plot it on your calculator, then use the appropriate utility in the CALC menu to determine the solution. Copy the plot and the results onto your homework paper. Exercises #17 and 23.
  • In Bittinger, page 175, find the slopes of the line indicated in exercises #27 and 28. Include units with your numerical answer.
  • In Bittinger, pages 176-177, determine the slope of the line in exercises #33, 37, 39, and 49.
• Assignment #21
  • In Bittinger, read Section 3.5, pages 179-186.
  • In Bittinger, page 187, explain why (or why not) the relations given in exercises #1 and 5 are functions.
  • In Bittinger, page 187-188, perform each of the following tasks for exercises #13, 15, 19, and 21.
    1. Make a copy of the given graph on graph paper.
    2. Indicate the solution in the manner shown in the graphs in Example 3, page 182.
  • In Bittinger, page 188, make a quick copy of the graphs in exercises #23, 25, 27, and 29, then indicate whether or not the graph represents a function. Justify your answer.
  • In Bitinger, page 188, evaluate the functions in exercises #31, 33, and 35 at each of the given values. Please arrange your work as follows:

    f(-1)=5(-1)2+4(-1)
         =5(1)+4(-1)
         =5-4
         =1
    

  • In Bittinger, page 188, #37 and 39, use the given function and a calculator to find the answer, correct to the nearest hundredth.
  • In Bittinger, page 189, use a calculator to draw the graph of the given function in exercise #45. Use the "value" utility in the CALC menu of your calculator to evaluate the function at the given speed.
  • In Bittinger, page 189, plot the data in exercise #47 on a sheet of graph paper, then make a "leap of faith" and draw the graph of a function that seemingly "fits" the data. Use your graph to answer the given question and indicate your reasoning on your graph in a manner similar to the second graph on page 186 of your text.
  • In Bittinger, page 190, do exercise #63.
• Assignment #22
  • In Bittinger, read Section 3.6, pages 191-196.
  • In Bittinger, page 196, answer the question in exercises #1 and 5.
  • In Bittinger, page 176, make a copy of the graph in exercises #7 and 9 on a sheet of graph paper. Project the points on the graph onto the x-axis and shade this "domain" in red, the project the points on the y-axis and shade this "range" in blue. Use both set-builder and interval notation to describe the domain and range in each exercise.
  • In Bittinger, page 197, use a graphing calculator to sketch the graph of the given equation in exercises 15 and 17. Copy the result onto your homework paper, then use the directions in the previous problem to shade the domain and range on the x and y-axis, respectively. Use both set-builder and interval notation to describe the domain and range.
  • In Bittinger, page 197, use an analytical technique to find the domain (set of "permissable x-values") in exercises #27, 31, 35, 37, and 39.
  • In Bittinger, page 198, determine a function to model the given model in exercises #45 and 47, then determine the "empirical" domain of the function .Note: The empirical domain is the set of all values that make "practical" sense in the equation. For example, in exercise #45, it makes no sense to talk about "negative" sales.
• Assignment #23
  • Reminders.
    1. Please remember to place the page and exercise numbers across the first line of your homework assignment.
    2. Draw all lines with a ruler.
  • In Bittinger, read Section 4.1, pages 208-214.
  • In Bittinger, use a graphing calculator and your knowledge of the slope and y-intercept to match the graphs with the equations provided in Exercise #19 on page 214.
  • In Bittinger, page 215, perform each of the following tasks for the equations provided in exercises #21, 29, 31, and 35.
    1. Place the equation in the form y = mx + b, then identify the slope and y-intercept.
    2. On a sheet of graph paper, use the slope and y-intercept to sketch the line having the given equation.
  • In Bittinger, page 215, exercise #39, perform each of the following tasks.
    1. On a sheet of graph paper, sketch the graph of the given equation.
    2. Use the graph to estimate the total cost of 6 months of service, then verify this result using the given equation.
  • In Bittinger, page 215, perform each of the following tasks for exercise #43.
    1. Use the given information to model the graph with an equation.
    2. Use a graphing calculator to graph the equation on its empirical domain, that is, the domain of values that make sense for this application. You may have to use analysis and the equation to help identify the empirical domain. Copy the resulting image onto your homework paper, label and scale each axis with xmin, xmax, ymin, and ymax. Use interval notation to describe the empirical domain.
  • In Bittinger, page 215, perform each of the following tasks for exercises #45 and 49.
    1. Write the real-world meaning of the slope in the given exercise. Include units with your answer.
    2. Write the real-world meaning of the y-intercept in the given exercise. Include units with your answer.
  • In Bittinger, page 216, match the given graphs with the descriptions in exercise #52.
• Assignment #24
  • Reminders.
    1. Please remember to place the page and exercise numbers across the first line of your homework assignment.
    2. Draw all lines with a ruler.
  • In Bittinger, read Section 4.2, pages 218-225.
  • In Bittinger, page 225, sketch the graphs of exercises #23 and 24 on a sheet of graph paper.
  • In Bittinger, page 225, perform each of the following tasks for the equations in exercises #39 and 45.
    1. Find the x and y-intercepts of the given equation.
    2. On a sheet of graph paper, plot the x and y-intercepts found in part (1) and draw a line through them. Label and scale each axis and label each intercept with its coordinates.
  • In Bittinger, page 226, use a graphing calculator to determine the viewing window the shows both the x and y-intercepts of the line reperesented by the equation in exercises #51 and 53. Copy the image onto your homework paper. Label each axis and scale the axes with the values of xmin, xmax, ymin, and ymax. Label the graph with its equation.
  • In Bittinger, page 226, place each equation in exercises #55 and 57 in the form y = mx + b. Use this form to identify the slope of each equation. Use the slopes to determine whether or not the lines are parallel.
  • In Bittinger, page 226, place each equation in exercises #61 and 63 in the form y = mx + b. Use this form to identify the slope of each equation. Use the slopes to determine whether or not the lines are perpendicular.
  • In Bittinger, page 226, perform each of the following tasks for exercises #65 and 67.
    1. Place the equation in the form y = mx + b, if not in that form already. Identify the slope and y-intercept.
    2. On a sheet of graph paper, use the slope and y-intercept found in part (1) to graph the given equation. Then plot the given point and draw a line through this point that is parallel to the first line.
    3. Label each line in your sketch with its equation. Label and scale each axis.
  • In Bittinger, page 226, perform each of the following tasks for exercises #73 and 75.
    1. Place the equation in the form y = mx + b, if not in that form already. Identify the slope and y-intercept.
    2. On a sheet of graph paper, use the slope and y-intercept found in part (1) to graph the given equation. Then plot the given point and draw a line through this point that is perpendicular to the first line.
    3. Label each line in your sketch with its equation. Label and scale each axis.
• Assignment #25
  • Reminders.
    1. Please remember to place the page and exercise numbers across the first line of your homework assignment.
    2. Draw all lines with a ruler.
  • In Bittinger, read Section 4.3, pages 227-234.
  • In Bittinger, page 234, perform each of the following tasks for exercises #3 and 7.
    1. On graph paper, sketch the line through the given point with the given slope.
    2. Label your line with the point-slope form of its equation y-y₀=m(x-x₀).
  • In Bittinger, page 234, perform each of the following tasks for exercises #15 and 16.
    1. On graph paper, sketch the line through the given point with the given slope.
    2. Extend your line, if necessary, so it crosses the y-axis. Estimate the coordinates of the y-intercept.
    3. Find the equation of the line in point-slope form y-y₀=m(x-x₀). Place this equation in slope-intercept form (y=x+b) by solving the equation for y. Label your graph with the slope intercept form of the line. Does the y-intercept indicated by the point slope form of the line agree with the answer found in part (2)? Note: Please perform all calculations on your graph paper next to your plot. Don't do your calculations in a separate location.
  • In Bittinger, page 234, perform each of the following tasks for exercises #23 and 29.
    1. On graph paper, sketch the line through the given points.
    2. Find the equation of the line in point-slope form y-y₀=m(x-x₀). Note: Please perform all calculations on your graph paper next to your plot. Don't do your calculations in a separate location.
  • In Bittinger, page 235, perform each of the following tasks for exercises #35 and 37.
    1. On graph paper, use the given data to draw the line modeling the problem statement. Label your axes with the variables given in the problem and scale each axis appropriately.
    2. Find a linear function that passes through the two given data points. Express your answer in the form y=mx+b, using of course the given variables in place of y and x. Use your equation to answer the question posed in part (b) of each exercise. Note: Please perform all calculations on your graph paper next to your plot. Don't do your calculations in a separate location.
    3. Use your graph to answer the question posed in part (b) of each exercise.
  • In Bittinger, page 236, perform each of the following tasks for exercise #43.
    1. Set up a coordinate axes on graph paper. Let x represent the number of years since 1987 and label the horizontal axis with x. Let B represent the average monthly phone bill and label the vertical axis B. Scale each axis so that you have a large graph (fitting an entire sheet of graph paper) that will fit all of the data. Plot the data from the given table on your coordinate system.
    2. Use a clear plastic ruler to draw the "line of best fit." Select two points on your line of best fit and label them with their coordinates. These must not be two of the given data points.
    3. Use the points approximated in part (2) to find the slope of the line of best fit. Include units with your answer and give a real-world description of what the slope actually represents in this problem. Note: Please perform all calculations on your graph paper next to your plot. Don't do your calculations in a separate location.
    4. Use the slope and either of the point approximations found in part (2) to find the equation of the line in point slope form y-y₀=m(x-x₀). Note: Please perform all calculations on your graph paper next to your plot. Don't do your calculations in a separate location.
    5. Replace y and x in the equation found in part (4) with B and x, respectively, then solve the resulting equation for B. This is the equation of the line of best fit. Note: Please perform all calculations on your graph paper next to your plot. Don't do your calculations in a separate location.
    6. Enter the given data in your calculator and use the linear regression utility to find the equation of the line of best fit. Label your line of best fit with this equation. How does it compare to the answer found in part (5)?
  • Assignment #26
    • In Bittinger, read Section 5.1, pages 274-279.
    • In Bittinger, page 280, do exercises #1-80, just the odd ones. Show All of your work in simplifying each exponential expression.
    • In Bittinger, page 280, simplify the exponential expressions in exercises #91 and 93. Show All of your work in simplifying each exponential expression.
    • In Bittinger, page 281, solve the equation in exercise #105. Show all of your work.
  • Assignment #27
    • In Bittinger, read Section 5.2, pages 282-292.
    • In Bittinger, page 292-293, follow the instructions in the text for exercises #17, 21, 23, 25, 27, 31, 33, 37, and 43.
    • In Bittinger, page 294, perform each of the following tasks for exercises #63, 67, and 69.
      1. Use your calculator to draw a sketch of the given polynomial. Adjust the Window parameters until all important behavior of the polynomial is evident in your viewing window (zeros, maximums, minimums, etc). Copy the imgage in your view screen onto your homework paper. Label each axis and scale each axis with xmin, xmax, ymin, and ymax.
      2. Use the zero or root finding routine in the CALC menu to find the zeros of each polynomial. Label these zeros in the plot in part (1) with their coordinates.
      3. Use the maximum and/or minimum routines in the CALC menu to find the turning points of the polynomials. Label each of these points in the plot in part (1) with their coordinates.
      4. Use both set-builder and interval notation to describe the domain and range of the polynomial function plotted in part (1).
    • In Bittinger, page 294-295, perform each of the following tasks for exercise #76.
      1. On a sheet of graph paper, label and scale each axis so that you have a "large plot" that will hold all of the data in the given table. Place the Ice Thickness on the horizontal axis (x-axis) and the Maximum Safe Load on the vertical axis (y-axis). Plot the data from the given table on your coordinate system.
      2. Using a pencil, "freehand" what you think to be the a quadratic (second degree) polynomial that "best fits" the plotted data.
      3. Load the data from the table into your calculator. Find the equation of the quadratic that "best fits" the given data. Label your plot in part (2) with this equation.
  • Assignment #28
    • In Bittinger, read Section 5.3, pages 296-303.
    • In Bittinger, page 303, simplify the expressions in exercises #7, 11, 31, and 33. Copy the expression down, then show any necessary work.
    • In Bittinger, page 304-305, after copying the given image onto your homework paper, follow the instructions given in exercises #41, 42, 45, 47, 50, and 51.
    • In Bittinger, page 305, simplify the expressions in exercises #63 and 65.
    • In Bittinger, page 305, after copying the figure in exercise #69, find the requested polynomial.
  • Assignment #29
    • In Bittinger, read Section 5.4, pages 306-314.
    • In Bittinger, page 314, simplify the expressions in exercises #35, 37, 41, 43, 65-79 odd. Copy the expression down, then show any necessary work.
    • In Bittinger, page 315-316, after copying the given image onto your homework paper, follow the instructions given in exercises #110, 111, 113, and 117.
    • In Bittinger, page 316, perform each of the following tasks for the word problems in exercises #120 and 127.
      1. Set up a variable dictionary telling what each variable represents.
      2. Set up an equation modeling the problem statement.
      3. Solve the equation.
      4. Answer the question.
      5. Look Back.
  • Assignment #30
    • In Bittinger, read Section 5.5, pages 317-322.
    • In Bittinger, page 322, evaluate the polynomial at the given values in exercise #1.
    • In Bittinger, page 323, simplify the expressions in exercises #27, 29, 31, 33, 37, 41, 45, and 49.
    • In Bittinger, page 324, after copying the given image onto your homework paper, find the area of the shaded region in exercises #51, 53, 55, 57. Simplify your answer.
    • In Bittinger, page 324, evaluate the functions in exercises #63 and 65 at the given values.
    • In Bittinger, page 325, copy the figure in exercises #77, 78, 79, and 80 onto your homework paper. Then find the area of the shaded regions.
    • In Bittinger, page 325, copy the figure in exercises #81 onto your homework paper. Then find the surface area of the given object.
  • Assignment #31
    • In Bittinger, read Section 5.6, pages 326-328. In Math 105, you are only responsible for the material on dividing by a monomial. Division by binomials and synthetic division will be covered in Math 120 or Math 30.
    • In Bittinger, page 333, do exercises $1-10.
  • Assignment #32
    • In Bittinger, read Section 5.7, pages 335-341.
    • In Bittinger, page 341-342, do exercises #1-96, odd.
  • Assignment #33
    • In Bittinger, read Section 6.1, pages 350-359.
    • In Bittinger, page 359-360, first copy the graph in exercises #1 and 3 onto your homework paper. Then, identify the solutions of the given equation.
    • In Bittinger, page 360, perform each of the following tasks for exercises #9 and 11.
      1. Use a graphing calculator to graph each side of the given equation. Adjust the viewing window so that all points of intersection of the two graphs are visible in the viewin window. Copy the result onto your homework paper. Label each axis and scale each axis with xmin, xmax, ymin, and ymax.
      2. Use the intersect utility from the CALC menu to find the points of intersection of the two graphs. Draw a number line below your graph, then drop dashed vertical lines from each point of intersection to your number line. Shade and label the x-values of the intersection points on your number line. Check each of these solutions in the given equation.
    • In Bittinger, page 360, perform each of the following tasks for exercises #21 and 23.
      1. Use a graphing calculator to sketch the given function. Adjust your viewing window so that all x-intercepts and "turning points" of the given polynomial function are visible in your viewing window. Copy the final image onto your homework paper. Label each axis, then scale each axis with xmin, xmax, ymin, and ymax.
      2. Use the root or zero utility in your CALC menu to find the zeros of the given polynomial. Draw a number line below your graph and drop dashed, vertical lines from each zero (x-intercept) to your number line. Shade and label these points on the number line. Check each of these in the function by hand to verify that they are indeed zeros of the given function.
    • In Bittinger, page 361, factor out the greatest common factor in each of the polynomials in exercises #35, 37, 41, 45, and 47.
    • In Bittinger, page 362, factor each of the given expressions in exercises #67, 69, 71, 73, 75, and 81.
    • In Bittinger, page 362, solve each of the given equations by hand in exercises #85, 87, 89, and 91.
  • Assignment #34
    • In Bittinger, read Section 6.2, pages 363-369.
    • In Bittinger, page 370, factor each expression completely in exercises #1-29 odd.
    • In Bittinger, page 370, perform each of the following tasks for exercises #41 and 43.
      1. Use a graphing calculator to sketch the given function. Adjust your viewing window so that all x-intercepts and "turning points" of the given polynomial function are visible in your viewing window. Copy the final image onto your homework paper. Label each axis, then scale each axis with xmin, xmax, ymin, and ymax.
      2. Use the root or zero utility in your CALC menu to find the zeros of the given polynomial. Draw a number line below your graph and drop dashed, vertical lines from each zero (x-intercept) to your number line. Shade and label these points on the number line. Check each of these in the function by hand to verify that they are indeed zeros of the given function.
      3. Find the zeros of each function using hand calculations only. Factor and use the zero product property, then compare your solutions to those found in part (2).
    • In Bittinger, page 370, perform each of the following tasks for the equations in exercises #45 and 51.
      1. Use a graphing calculator to graph each side of the given equation. Adjust the viewing window so that all points of intersection of the two graphs are visible in the viewin window. Copy the result onto your homework paper. Label each axis and scale each axis with xmin, xmax, ymin, and ymax.
      2. Use the intersect utility from the CALC menu to find the points of intersection of the two graphs. Draw a number line below your graph, then drop dashed vertical lines from each point of intersection to your number line. Shade and label the x-values of the intersection points on your number line. Check each of these solutions in the given equation.
      3. Using hand calculations only, find the solution of the given equation. Use factoring, then the zero product property, then compare your solutions with those from part (2).
    • In Bittinger, page 370, use the given graph to help factor the polynomial in exercise #55.
    • In Bittinger, page 370, perform each of the following tasks for exercise #57.
      1. Use a graphing calculator to draw the given polynomial. Adjust the viewing window so that all x-intercepts and "turning points" are visible in the viewing window. Copy the final graph onto your homework paper. Label each axis, then scale each axis with xmin, xmax, ymin, and ymax.
      2. Use the zero or root finding utility in the CALC menu to find the zeros of the given function. Mark these on a number line below your graph in the "usual manner."
      3. Use the zeros found in part (2) to factor the given polynomial. Check your result with multiplication.
    • In Bittinger, page 370, perform each of the following tasks for the zeros given in exercises #57 and 61.
      1. Find a polynomial having the given zeros.
      2. Use a graphing calculator to plot the polynomial found in part (1). Adjust the viewing window so that all zeros and "turning points" are visible in the viewing window. Copy the final result onto your homework paper, label each axis, then scale each axis with xmin, xmax, ymin, and ymax.
    • In Bittinger, page 371, perform each of the following tasks for exercise #75.
      1. Copy the given graph onto a sheet of graph paper. Draw a number below your graph and shade and label the solutions of x²-2x-3=0 in the "usual manner."
      2. Copy the given graph onto a sheet of graph paper a second time. Draw a number below your graph and shade and label the solutions of x²-2x-3< 5 in the "usual manner."
      3. In Bittinger, page 371, exercis #77, find a polynomial having the given zeros. Plot your result on your calculator. Adjust the viewing window so that all zeros and "turning points" are visible in your view screen. Copy the result onto your homework paper in the "usual manner."
  • Assignment #35
    • In Bittinger, read Section 6.3, pages 373-379.
    • In Bittinger, page 379, factor each expression completely in exercises #1-27 odd.
    • In Bittinger, page 379, perform each of the following tasks for exercises #35 and 37.
      1. Use a graphing calculator to sketch the given function. Adjust your viewing window so that all x-intercepts and "turning points" of the given polynomial function are visible in your viewing window. Copy the final image onto your homework paper. Label each axis, then scale each axis with xmin, xmax, ymin, and ymax.
      2. Use the root or zero utility in your CALC menu to find the zeros of the given polynomial. Draw a number line below your graph and drop dashed, vertical lines from each zero (x-intercept) to your number line. Shade and label these points on the number line. Check each of these in the function by hand to verify that they are indeed zeros of the given function.
      3. Find the zeros of each function using hand calculations only. Factor and use the zero product property, then compare your solutions to those found in part (2).
    • In Bittinger, page 379, perform each of the following tasks for the equations in exercises #39 and 41.
      1. Use a graphing calculator to graph each side of the given equation. Adjust the viewing window so that all points of intersection of the two graphs are visible in the viewin window. Copy the result onto your homework paper. Label each axis and scale each axis with xmin, xmax, ymin, and ymax.
      2. Use the intersect utility from the CALC menu to find the points of intersection of the two graphs. Draw a number line below your graph, then drop dashed vertical lines from each point of intersection to your number line. Shade and label the x-values of the intersection points on your number line. Check each of these solutions in the given equation.
      3. Using hand calculations only, find the solution of the given equation. Use factoring, then the zero product property, then compare your solutions with those from part (2).
    • In Bittinger, page 379-380, Use an algebraic technique to find the domain of the functions in exercises #51 and 53.
  • Assignment #36
    • In Bittinger, read Section 6.4, pages 380-386.
    • In Bittinger, page 386-387, factor each expression completely in exercises #1-50 odd.
    • In Bittinger, page 387, perform each of the following tasks for exercises #55 and 65.
      1. Use a graphing calculator to sketch each side of the given equation. Adjust your viewing window so that all point(s) of intersection are visible in your viewing window. Copy the final image onto your homework paper. Label each axis, then scale each axis with xmin, xmax, ymin, and ymax.
      2. Use the intersect utility in your CALC menu to find the points of intersection of the two graphs. Draw a number line below your graph and drop dashed, vertical lines from each pont of intersection to your number line. Shade and label these points on the number line.
      3. Find the solutions of each equation using hand calculations only. Factor and use the zero product property, then compare your solutions to those found in part (2).
    • In Bittinger, page 387, perform each of the following tasks for the equations in exercises #57, 59, and 63.
      1. Use a graphing calculator to graph the polynomial on the left side of the given equation. Adjust the viewing window so that all "turning points" and x-intercepts are visible in the viewin window. Copy the result onto your homework paper. Label each axis and scale each axis with xmin, xmax, ymin, and ymax.
      2. Use the zero or root finding utility from the CALC menu to find the zeros of the function.. Draw a number line below your graph, then drop dashed vertical lines from each x-intercept to your number line. Shade and label the x-values of the x-intercepts on your number line.
      3. Using hand calculations only, find the solution of the given equation. Use factoring, then the zero product property, then compare your solutions with those from part (2).
    • In Bittinger, page 387, perform each of the following tasks for the equations in exercises #67 and 71,
      1. Use a graphing calculator to graph the polynomial on the left side of the given equation. Adjust the viewing window so that all "turning points" and x-intercepts are visible in the viewin window. Copy the result onto your homework paper. Label each axis and scale each axis with xmin, xmax, ymin, and ymax.
      2. Use the zero or root finding utility from the CALC menu to find the zeros of the function.. Draw a number line below your graph, then drop dashed vertical lines from each x-intercept to your number line. Shade and label the x-values of the x-intercepts on your number line.
      3. Try factoring the polynomial on the left of the equation to convince yourself that the given polynomial doesn't factor. This is a situation where your only recourse is to find the zeros using a graphing calculator.
    • In Bittinger, page 387, factor completely the polynomials given in exercises #85, 87, 91, 93, 97, and 105.
  • Assignment #37
    • In Bittinger, read Section 6.5, pages 389-397.
    • In Bittinger, page 397-398, solve each of the word problems in exercises #1, 3, 5, 7, 9, 13, 14, and 17. Follow the usual rubric for word problems.
      1. Set up a variable dictionary indicating what each variable represents. In the case of these particular problems, this is probably best done by drawing a figure, then indicating on the figure what each variable represents.
      2. Set up an equation modeling the problem statement.
      3. Solve the equation.
      4. Answer the question with a complete sentence.
      5. Look back. Explain why your solution makes sense and satisfies the constraints posed in the problem statement.
  • Assignment #38
    • In Bittinger, read Section 8.1, pages 470-476.
    • In Bittinger, page 477, perform each of the following tasks for the systems given in exercises #27, 29, 31, 33, 35, and 36.
      1. On graph paper, sketch the line represented by each equation. Note: One of two methods is recommened: (1) Solve the equation for y, putting the equation in the form y=mx+b, then use the slope m and y-intercept b to graph the equation, or (2) place the equation in the form Ax+By=C, then use Michele Olsen's "finger method" to find the x and y-intercepts (let x=0 and find y, then let y=0 and find x. Plot the intercepts then draw the line passing through the intercepts.
      2. Label the point of intersection of the two lines with its coordinates. This is the solution for the given system of equations.
    • In Bittinger, page 477, perform each of the following tasks for the systems in exericses #45 and 53.
      1. Solve each equation for y to put the equation in the form y=max+b.
      2. Enter the equations from part (1) into your graphing calculator and graph. Adjust the window parameters so that the point of intersection is visible in the viewing window. Copy the result onto your homework. Label and scale each axis with xmin, xmax, ymin, and ymax.
      3. Use the intersect utility in the CALC menu to find the point of intersection of the two lines. Label the point of intersection with its coordinates on the plot from part (2). This is the solution to the system given in the exercise.
  • Assignment #39
    • In Bittinger, read Section 8.2, pages 480-485.
    • In Bittinger, page 486, use the substitution method to solve the systems in exercises #3, 5, 9, and 13. We don't want to see endless lines of calculations crammed together.Make sure that you do the following.
      1. Label equations that will be referenced in upcoming steps.
      2. Let your readers know what you are doing at each step. For example, "Substitute equation (3) in equation (1)."
      3. Skip lines to break up your presentation.
    • In Bittinger, page 486, use the elimination method to solve the systems in exercises #21, 23, 25 and 29. Be sure to follow the suggestion above.
    • In Bittinger, page 486, perform each of the following tasks for the system of linear equations in exercise #34.
      1. Sketch the system on a sheet of graph paper and estimate the coordinates of the point of intersection. Place these estimated coordinates on your plot near the point of intersection of your two lines.
      2. Use a graphing calculator to solve the system. Sketch the lines, then use the intersect utitlity in the CALC menu to find the coordinates of the point of intersection. Use the >Frac utility in the MATH menu to change the approximations into rational form. Place these fractions on your plot above.
      3. Use the substitution method to find the exact solution of the system in rational (fraction) format.
      4. Use the elimination method to find the exact solution of the system in rational (fraction) format.
      5. Compare solutions from the alternate techniques above.
    • In Bittinger, page 487, solve the systems in exercises #61 and 63. Find exact solutions using either the substitution or elimination methods.