Name: _________________________________________
Algebra 2/Trig – Unit 8: Relations and Functions REVIEW SHEET
DATE:_________
PERIOD:_______
1. The accompanying graph shows the curves of best fit for data points comparing temperature to altitude in four
different regions, represented by the relations A, B, C, and D.
Which relation is not a function?
(1) A
(3) C
(2) B
(4) D
2. Given the relation
, which value of k will result in the relation not being a function?
1) 1
2) 2
3) 3
4) 4
3. Based on the graph of the function 𝑓 above, what are the values of 𝑥 for which 𝑓(𝑥) is negative?
(A) −6 < 𝑥 < 0
(B) 0 < 𝑥 < 6
(C) 6 < 𝑥 < 7
(D) −6 < 𝑥 < 6
(E) −6 < 𝑥 < 0 and 6 < 𝑥 < 7
4. If the point (x,y) lies on the graph y  f ( x) , the graph of y  f
(1) (-x,-y)
(3) (y,x)
(2) (-y,-x)
(4) ( , )
1 1
x y
1
( x) must contain point
5. A function is defined by the equation y 
(1) y  2 x  3
(3) y  2 x 
3
2
(2) y  2 x  3
(4) y  2 x 
3
2
1
3
x  . Which equation defines the inverse of this function?
2
2
6. What is the range of the function shown below?
1)
2)
3)
4)
7. If
1) domain:
2) domain:
, what are its domain and range?
; range:
; range:
3) domain:
4) domain:
; range:
; range:
8. If
9. If
10. If
, express
and
in simplest form.
, evaluate
and
1)
2)
3)
4)
11. If 𝑓(𝑥) = 5𝑥 − 4, find 𝑓 −1 (6)
.
, which expression is equivalent to
?
12. The accompanying diagram shows the graph of the line whose equation is y  
On the same set of axes, sketch the graph of the inverse of this function.
State the coordinates of a point on the inverse function.
13. Which relation is a function?
(1) xy  7
(3) x 2  y 2  7
(2) x  7
(4) x 2  y 2  7
14. Determine if the following functions are one-to-one, onto, both, or neither.
a 𝑓(𝑥) = 𝑥 3 + 1
b
1
x  2.
3