Unit 3 Functions Review
1. Determine whether each relation is a function, then state the domain and range.
a) {(−1,9), (0,4), (1,9), (2,7)}
c) {(−1,5), (0,5), (1,4), (1,9)}
b) 𝑦 = 2𝑥 − 3
Function: Yes / No
Function: Yes / No
Function: Yes / No
Domain:
Domain:
Domain:
Range:
Range:
Range:
d)
e)
f)
Function: Yes / No
Function: Yes / No
Function: Yes / No
Domain:
Domain:
Domain:
Range:
Range:
Range:
2. If 𝑓(𝑥) = 3(𝑥 + 2)2 − 1 and 𝑔(𝑥) =
a) 𝑓(3) − 𝑔(2)
2
2𝑥+1
+ 3, find
b) 2𝑓(1)
c) x if 𝑔(𝑥) = 1
3. Given the information, fill in the missing parts of the table.
Basic
Equation
Horizontal
Shift
Vertical
Shift
Horizontal
Stretch
Vertical
Stretch
𝑦 = √𝑥
Right 2
Down 1
2
3
𝑦 = 𝑥2
Left 5
Up 3
1
3
-4
1
𝑥
Right 3
Up 6
-1
1
2
Left 1
Down 7
0.5
-2
𝑦=
𝑦 = 𝑓(𝑥)
Equation
1
𝑦 = 2√ 𝑥 + 5 − 1
2
𝑦=
−2
+8
3𝑥 − 4
𝑦 = 2(−2𝑥 + 6)2 − 5
4. On a separate piece of graph paper, sketch the following graphs. State their domain and range.
a) 𝑦 = −3√−𝑥 − 4 + 7
b) 𝑦 = √2𝑥 + 6 − 1
2
Domain:
Domain:
c) 𝑦 = −2(2(𝑥 − 5)) + 1
Domain:
Range:
Range:
Range:
e) 𝑦 =
6
3𝑥−12
+4
f)
1
2
𝑦 = ( 𝑥) − 2
g) 𝑦 =
2
1
2𝑥+6
d) 𝑦 =
Domain:
Range:
−2
2
𝑥+2
Domain:
Domain:
Domain:
Range:
Range:
Range:
Range:
5. Determine an equation of the graphs below.
Equation
Equation
6. Apply the given transformations on the functions 𝑦 = 𝑓(𝑥).
1
Given 𝑦 = 𝑓(𝑥), graph 𝑦 = −𝑓(2𝑥 − 2) + 3
Given 𝑦 = 𝑓(𝑥), graph 𝑦 = 2𝑓 (− 𝑥) − 1
2
7. Graph the inverse for the given function 𝑦 = 𝑓(𝑥). Is the inverse a function? Describe why/why not.
8. Algebraically determine the inverse equations for each. State the domain and range for the inverse
relation/function.
a. 𝑦 = 2(𝑥 − 2)2 + 6
b. 𝑦 = −√2(𝑥 − 5) + 1
c.
𝑦=
2
𝑥−4
+3
1
1
2
2
h) 𝑦 = − √ (𝑥 + 1)
Domain:
Equation
−3