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 functionG(x) = x +3/2 is the inverse ofF(x) = 2x- 3.

Step 1:The function notationF(x)can be written as a variable in an equation. Is that variablexory? WriteF(x) = 2x- 3as an equation with your chosen variable.(2 points)

Step 2:Switch the variables in the equation from Step 1. Then solve fory. Show your work.(2 points)

Step 3:Show thatis the inverse ofF(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 ofF(x) is shown below. On the same grid, draw the graph of the inverse ofF(x).(2 points)

Part II:Is the inverse a function? Explain your answer.(3 points)

3.SupposeF(x) = x^2 and G(x) = 5(x3)^2 + 2

Part I:The graph ofF(x) is shown below. On the same grid, draw the graph ofG(x).(3 points)

Part II:Describe how the graph ofG(x) relates to the graph ofF(x).(5 points)

4.Draw lines to match each pair of functions to the phrase that best describes the difference betweenF(x) andG(x).(4 points)

FunctionsF(x) andG(x)		Difference betweenF(x) andG(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 ofF(x), shown below, resembles the graph ofG(x)=x2, but it has been flipped over thex-axis,stretched vertically by a factor of 3, shifted down 4 units, and left 1 unit.

Part I:Write the equation ofF(x).(6 points)

Part II:Explain how you arrived at the equation fromPart I.(4 points)

6.The graph ofF(x) is shown below. SupposeG(x) has the same shape as the graph ofF(x), but is shifted down 3 units and left 2 units.

"A graph with x-axis and y-axis marking from negative 5 to plus 5. A W-shaped curve line is drawn from quadrants two to one by intersecting points in quadrants three and four. first, intersect point at (-1.8,0) in axis and the second point at (-1.8,2) in quadrant three, third point is marked at (1,2) in quadrant four mentioned with a formula F(x) and the last point is marked at (1.8,0) on x-axis forming a W shape."

Part II:Explain how you arrived at the graph fromPart I.(4 points)

7.Roger has the graph ofF(x) = 4x²but needs to sketch the graph ofG (x)= (x+3)2 + 2/3. Describe how Roger can use the graph ofF(x) to sketch the graph ofG(x).(7 points)