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Function Homework -- Homework: Graphing

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides practice problems designed to develop some concepts related to graphing.

Note: You are viewing an old version of this document. The latest version is available here.

The following graph shows the temperature throughout the month of March. Actually, I just made this graph up—the numbers do not actually reflect the temperature throughout the month of March. We’re just pretending, OK?

Figure 1
A graph shows the temperature throughout the month of March

Exercise 1

Give a weather report for the month of March, in words.

Exercise 2

On what days was the temperature exactly 0 ° C 0 ° C size 12{0°C} {} ?

Exercise 3

On what days was the temperature below freezing?

Exercise 4

On what days was the temperature above freezing?

Exercise 5

What is the domain of this graph?

Exercise 6

During what time periods was the temperature going up?

Exercise 7

During what time periods was the temperature going down?

Exercise 8

Mary started a company selling French Fries over the Internet. For the first 3 days, while she worked on the technology, she lost $100 per day. Then she opened for business. People went wild over her French Fries! She made $200 in one day, $300 the day after that, and $400 the day after that. The following day she was sued by an angry customer who discovered that Mary had been using genetically engineered potatoes. She lost $500 in the lawsuit that day, and closed up her business. Draw a graph showing Mary’s profits as a function of days.

Exercise 9

Fill in the following table. Then draw graphs of the functions y=x2y=x2 size 12{y=x rSup { size 8{2} } } {}, y=x2+2y=x2+2 size 12{y=x rSup { size 8{2} } +2} {}, y=x21y=x21 size 12{y=x rSup { size 8{2} } - 1} {}, y=(x+3)2y=(x+3)2 size 12{y= \( x+3 \) rSup { size 8{2} } } {}, y=2x2y=2x2 size 12{y=2x rSup { size 8{2} } } {}, and y=x2y=x2 size 12{y= - x rSup { size 8{2} } } {}.

Table 1
xx x 2 x 2 size 12{x rSup { size 8{2} } } {} x 2 + 2 x 2 + 2 size 12{x rSup { size 8{2} } +2} {} x 2 1 x 2 1 size 12{x rSup { size 8{2} } - 1} {} ( x + 3 ) 2 ( x + 3 ) 2 size 12{ \( x+3 \) rSup { size 8{2} } } {} 2x 2 2x 2 size 12{2x rSup { size 8{2} } } {} x 2 x 2 size 12{ - x rSup { size 8{2} } } {}
-3            
-2            
-1            
0            
1            
2            
3            

Now describe in words what happened…

  • a. How did adding 2 to the function change the graph?
  • b. How did subtracting 1 from the function change the graph?
  • c. How did adding three to xx change the graph?
  • d. How did doubling the function change the graph?
  • e. How did multiplying the graph by –1 change the graph?
  • f. By looking at your graphs, estimate the point of intersection of the graphs y=x2y=x2 size 12{y=x rSup { size 8{2} } } {} and y=(x+3)2y=(x+3)2 size 12{y= \( x+3 \) rSup { size 8{2} } } {}. What does this point represent?

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