Answer the following questions using what you've learned from this unit. Write your answers in the space provided. Be sure to show all work.
1. Show that the function is the inverse of F(x) = 2x – 3.
Step 1: The function notation F(x) can be written as a variable in an equation. Is that variable x or
y?
Write F(x) = 2x – 3 as an equation with your chosen variable. (2 points)
Step 2: Switch the variables in the equation from Step 1. Then solve for y. Show your work.
(2 points)
Step 3: Show that is the inverse of F(x) = 2x – 3. Write your answer in inverse
notation. (2 points)2. Graph the inverse of the function, then determine if the inverse is a function.
Part I: The graph of F(x) is shown below. On the same grid, draw the graph of the inverse of F(x).
(2 points)
Part II: Is the inverse a function? Explain your answer. (3 points)
3. Suppose and
Part I: The graph of F(x) is shown below. On the same grid, draw the graph of G(x). (3 points)Part II: Describe how the graph of G(x) relates to the graph of F(x). (5 points)
4. Draw lines to match each pair of functions to the phrase that best describes the difference
between F(x) and G(x). (4 points)
Functions F(x) and G(x) Difference between F(x)
and G(x)
A. 1. Vertical compression
B. 2. Vertical shift of 5 units
up
C. 3. Vertical stretch
D. 4. Shift to the right of 5
units
5. The graph of F(x), shown below, resembles the graph of , but it has been flipped over the
x-axis, stretched vertically by a factor of 3, shifted down 4 units, and left 1 unit. Part I: Write the equation of F(x). (6 points)
Part II: Explain how you arrived at the equation from Part I. (4 points)