Unit 5 Review – Functions and Graphing
Name: ___________________________
1. Given 𝑓(𝑥) = 3𝑥 − 4 and 𝑔(𝑥) = −2𝑥 2 , perform the indicated operation:
(a) 𝑓(𝑥) + 𝑔(𝑥) =
(e) (𝑔 ∘ 𝑓)(𝑥) =
(b) (
𝑓
) (𝑥) =
𝑔
(f) 𝑓(𝑔(𝑥)) =
𝑥 ≠ _______
(g) (𝑓 − 𝑔)(2) =
(c) 𝑓(𝑥) − 𝑔(𝑥) =
(h) 𝑓(𝑔(1)) =
(d) (𝑓 ∙ 𝑔)(𝑥) =
2. Use the graphs to answer the following questions.
Domain:
Range:
Is this graph a function?
YES or NO
Is the inverse a function?
YES or NO?
Domain:
Range:
Is this graph a function?
YES or NO
Is the inverse a function?
YES or NO?
Domain:
Range:
Is this graph a function?
YES or NO
Is the inverse a function?
YES or NO?
Domain:
Range:
Is this graph a function?
YES or NO
Is the inverse a function?
YES or NO?
3. Find the inverse of the following functions:
(a) 𝑓(𝑥) = {(−5,9), (−1,2), (3,3), (8,4)}
(b) 𝑔(𝑥) = 𝑥 2 − 3
1
(c) ℎ(𝑥) = − 𝑥 + 1
2
4. Determine if the following functions are inverses. Must show work to receive credit.
1
2
5
5
(a)
𝑓(𝑥) = 𝑥 −
(b)
ℎ(𝑥) = (𝑥 − 3)2
𝑔(𝑥) = 5𝑥 + 2
YES or NO
𝑝(𝑥) = √𝑥 + 3
YES or NO
5. Find the inverse of 𝑝(𝑥) = 3𝑥 − 2.
6. The formula for the volume of a cylinder is 𝑉 = 𝜋𝑟 2 ℎ.
If the height of the cylinder is 10 inches then the
Then graph the function and its inverse.
volume of the cylinder would be 𝑉 = 10𝜋𝑟 2 .
(a) Find the inverse of this function.
(b) Use the inverse to find the radius of a cylinder if the
volume is 785 cubic inches.
7. Evaluate the graph at the specified domain.
𝑓(−6) = _____
𝑓(0) = _____
𝑓(2) = _____
𝑓(5) = _____
8. Write an equation for each piecewise graph.
9. Graph each piecewise function.
10. Critical Thinking: Write 𝑓(𝑥) = |𝑥| + 2 as a piecewise function. (Hint: Graph it first)