Functions Review
Algebra 2 and Trigonometry
Name:
1.
Date:
Which statement is true about the relation shown
on the graph below?
3.
Which diagram represents a one-to-one function?
A.
B.
C.
A.
It is a function because there exists one
x-coordinate for each y-coordinate.
B.
It is a function because there exists one
y-coordinate for each x-coordinate.
C.
It is not a function because there are multiple
y-values for a given x-value.
D.
D. It is not a function because there are multiple
x-values for a given y-value.
2.
Given the relation
R = f( 2; 3); (a; 4); (1; 9); (0; 7)g. Which
placement for a makes this relation a function
A.
1
B.
2
C.
0
D. 4
page 1
4.
On the accompanying diagram, draw a mapping
of a relation from set A to set B that is not a
function. Explain why the relationship you drew
is not a function.
5.
Which relation represents a function?
9.
The accompanying graph shows the heart rate, in
beats per minute, of a jogger during a 4-minute
interval.
What is the range of the jogger's heart rate during
this interval?
A.
f(0; 3); (2; 4); (0; 6)g
B.
f( 7; 5); ( 7; 1); ( 10; 3); ( 4; 3)g
A.
0–4
B.
C.
f(2; 0); (6; 2); (6; 2)g
C.
0–110
D. 60–110
1–4
D. f( 6; 5); ( 3; 2); (1; 2); (6; 5)g
6.
What is the domain of the function f (x) = p
over the set of real numbers?
7.
8.
A.
fx j x = 1g
B.
C.
fx j x < 1g
D. fx j x > 1g
10.
4
x+1
Which graph illustrates the relationship x varies
directly as y ?
A.
B.
C.
D.
1g
fx j x
p
What is the domain of the function f (x) = 3x + 7 ?
A.
xjx
C.
xjx
3
7
3
7
B.
xjx
D.
xjx
7
3
7
3
11.
A function is de ned by the equation y = 8x 3.
If the domain is 2 x 4, nd the minimum
value in the range of the function.
Algebra 2 and Trigonometry
page 2
If y varies directly as x and y = 32 when x = 4,
nd the value of y when x = 5.
Functions Review
12.
13.
14.
If x varies directly as y and x = 3 when y = 15,
nd the value of x when y = 25
Which equation shows that p varies inversely as q ?
A.
p = 10q
B.
pq = 10
C.
p = 10 + q
D. q = p2 + 10
The interest on a loan varies directly as the rate.
If the rate is halved, then the interest
A.
is halved
B.
is doubled
C.
remains the same
D. is multiplied by 4
19.
Which graph represents an inverse variation
between all values of x and y ?
A.
B.
C.
D.
If x varies inversely as y and x = 4 when y = 8,
nd x when y = 1.
15.
If x varies inversely as y and x = 2:5 when y = 40,
nd y when x = 2.
16.
Given: t travels inversely as p. If p is divided
by 2, then t is
17.
18.
A.
increased by 2
B.
C.
divided by 2
D. multiplied by 2
20.
decreased by 2
Every year a band is paid $350 to play at the
county fair. Let a represent the amount each
member receives and let n represent the number
of members in the band. The inverse variation
relationship between a and n is best represented as
A.
350 1
=
a
n
B.
C.
a + n = 350
D. an = 350
Algebra 2 and Trigonometry
21.
n
= 350
a
page 3
Which is an equation of the line that passes
through the point (1; 4) and has a slope of 3?
y = 13 x + 4
A.
y = 3x + 4
B.
C.
y = 3x
D. y = 3x + 1
1
Which is an equation of the line that passes
through the point (5; 2) and has a slope of 3?
A.
y = 3x
13
C.
y = 3x + 13
B.
y = 3x
13
D. y = 3x + 13
Functions Review
22.
23.
Which equation represents a line that has a slope
of 34 and passes through the point (2; 1)?
If point (a; b) lies on the graph y = f (x), the graph
y = f 1 (x) must contain point
A.
3y = 4x
5
B.
3y = 4x + 2
A.
(b; a)
B.
C.
4y = 3x
2
D. 4y = 3x + 5
C.
(0; b)
D. ( a; b)
28.
Which function is one-to-one?
A.
C.
24.
27.
f (x) = jxj
f (x) =
x2
B.
(a; 0)
Given the relation A: f(3; 2); (5; 3); (6; 2); (7; 4)g
Which statement is true?
f (x) = 2x
D. f (x) = sin x
A.
f( 2; 6); (3; 4); ( 7; 5)g
B.
f(2; 6); ( 3; 4); (7; 5)g
C.
f(6; 2); (4; 3); ( 5; 7)g
Both A and A
B.
Neither A nor A
C.
Only A is a function.
D. Only A
The inverse function of f(2; 6); ( 3; 4); (7; 5)g
is
1
A.
1
are functions.
1
is a function.
is a function.
29.
The function, f , is drawn on the accompanying set
of axes. On the same set of axes, sketch the graph
of f 1 , the inverse of f .
30.
If f (x) = x2
6, nd f
31.
If f (x) = 5x
2 and g(x) =
D. f( 6; 2); ( 4; 3); (5; 7)g
25.
26.
The inverse of the function 2x + 3y = 6 is
2
3x
+2
A.
y=
C.
y = 32 x + 2
B.
y=
3
2x
+3
D. y = 23 x + 3
What is the inverse relation of the function whose
equation is y = 3x 2?
A.
y=x
C.
y = 2x
B.
3
Algebra 2 and Trigonometry
1 (x).
y = 3x + 2
D. y =
x+2
3
page 4
p
3
x, evaluate (f g)( 8).
Functions Review
32.
33.
If f (x) = x2 and g(x) = x + 1, what is (f
If f (x) = 3x
f (3) g(2).
4 and g(x) = x2 ,
35.
g)(2)?
If f (x) =
A.
x2 + 3x + 6
B.
9x2 + 30x + 26
C.
3x2 + 8
D. 9x2 + 26
nd the value of
36.
34.
If f and g are two functions de ned by
f (x) = 3x + 5 and g(x) = x2 + 1, then g(f (x)) is
2
1
If f (x) =
and g(x) = , then (g f )(x) is
x+3
x
equal to
A.
1 + 3x
2x
B.
2x
1 + 3x
C.
x+3
2
D.
x+3
2x
x3
p
and g(x) = 3 x, nd f (g(9)).
3
Algebra 2 and Trigonometry
page 5
Functions Review
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Algebra 2 and Trigonometry
Functions Review
11/13/2014
1.
Answer:
C
21.
Answer:
C
2.
Answer:
D
22.
Answer:
C
3.
Answer:
C
23.
Answer:
B
4.
Answer:
[task]
24.
Answer:
C
5.
Answer:
D
25.
Answer:
B
6.
Answer:
D
26.
Answer:
D
7.
Answer:
B
27.
Answer:
A
8.
Answer:
13
28.
Answer:
C
9.
Answer:
D
29.
Answer:
10.
Answer:
B
11.
Answer:
30.
Answer:
p
x+6
40
12.
Answer:
31.
Answer:
12
5
13.
Answer:
32.
Answer:
9
A
14.
Answer:
33.
Answer:
1
32
15.
Answer:
34.
Answer:
3
50
16.
Answer:
35.
Answer:
B
D
17.
Answer:
36.
Answer:
C
D
18.
Answer:
B
19.
Answer:
D
20.
Answer:
D
connecting the points (4; 3), (3; 1), and
( 2; 1) is drawn