Practice Test Problems Chapter 1
Graph the given functions on the same rectangular coordinate
system. Describe how the graph of g is related to the graph of f.
16) f(x) = x, g(x) = x + 3
Give the domain and range of the relation.
1) {(4, -1), (7, 2), (8, -7), (8, 6)}
2) {(9, 8), (-6, -4), (-7, -5), (4, 5)}
6
y
5
3) {(-1, -4), (-2, -3), (-2, 0), (7, 3), (23, 5)}
4
3
Determine whether the relation is a function.
4) {(-1, -2), (3, -4), (6, -7), (7, 9), (11, -3)}
2
1
2
3
4
5
6 x
1
2
3
4
5
6 x
1
2
3
4
5
6 x
-6 -5 -4 -3 -2 -1
-1
5) {(-6, -8), (-6, -5), (1, 2), (3, -1), (8, 8)}
1
-2
-3
6) {(-7, -2), (-4, -4), (1, -2), (3, -7)}
-4
-5
-6
Determine whether the equation defines y as a function of x.
7) x2 + y = 9
17) f(x) = -2x, g(x) = -2x - 2
8) x + y2 = 1
6
y
5
9) x2 + y2 = 4
4
3
10) y2 = 4x
2
1
-6 -5 -4 -3 -2 -1
-1
11) x = y2
-2
-3
Evaluate the function at the given value of the independent
variable and simplify.
12) f(x) = 5x2 + 2x + 3; f(x - 1)
13) h(x) = x - 13 ;
h(19)
14) f(x) = x + 13;
f(-4)
-4
-5
-6
18) f(x) = x , g(x) = x - 1
6
y
5
4
15) f(x) = x2 + 5
x3 - 3x
;
3
f(-5)
2
1
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
1
22)
Use the vertical line test to determine whether or not the graph
is a graph in which y is a function of x.
19)
y
y
x
x
Use the graph to find the indicated function value.
23) y = f(x). Find f(1)
20)
y
5
y
4
3
2
1
x
-5
-4
-3
-2
-1
1
2
3
4
5 x
1
2
3
4
5 x
-1
-2
-3
-4
-5
21)
y
24) y = f(x). Find f(-4)
5
y
4
3
x
2
1
-5
-4
-3
-2
-1
-1
-2
-3
-4
-5
2
Use the graph to determine the functionʹs domain and range.
25)
6
Identify the intercepts.
28)
y
y
10
5
4
5
3
2
1
-10
-6 -5 -4 -3 -2 -1
-1
1
2
3
4
5
-5
5
10
x
5
10
x
5
10
x
6 x
-5
-2
-3
-4
-10
-5
-6
29)
y
10
26)
6
y
5
5
4
3
-10
-5
2
-5
1
-6 -5 -4 -3 -2 -1
-1
1
2
3
4
5
6 x
-10
-2
-3
-4
30)
-5
y
-6
10
5
27)
6
y
-10
5
-5
4
-5
3
2
-10
1
-6 -5 -4 -3 -2 -1
-1
1
2
3
4
5
6 x
-2
Find and simplify the difference quotient -3
-4
for the given function.
31) f(x) = 7x2
-5
-6
32) f(x) = x2 + 9x - 8
3
f(x + h) - f(x)
, h≠ 0
h
38) Decreasing
Evaluate the piecewise function at the given value of the
independent variable.
33)
-3x - 5 if x < -1
f(x) =
2x + 4 if x ≥ -1
y
8
4
Determine f(-4).
-12
-6
6
34)
12
x
-4
x - 3 if x > -2
f(x) =
-(x - 3) if x ≤ -2
-8
Determine f(-3).
The graph of a function f is given. Use the graph to answer the
question.
39) Find the numbers, if any, at which f has a relative
maximum. What are the relative maxima?
35)
x2 + 3
if x ≠ 3
g(x) = x - 3
x + 2 if x = 3
5
y
4
Determine g(3).
3
2
Identify the intervals where the function is changing as
requested.
36) Increasing
1
-5
-4
-3
-2
-1
1
2
3
4
5 x
-1
y
-2
8
-3
-4
4
-5
-12
-6
6
12
x
Use the graph of the given function to find any relative
maxima and relative minima.
40) f(x) = x3 - 3x 2 + 1
-4
5
-8
y
4
3
37) Constant
2
5
1
y
4
-5
-4
-3
-2
-1
1
-1
3
-2
2
-3
1
-4
-5
-4
-3
-2
-1
1
2
3
4
5 x
-5
-1
-2
-3
-4
-5
4
2
3
4
5 x
41) f(x) = x3 - 12x + 2
47)
20
y
y
10
16
8
12
6
4
8
2
4
-5
-4
-3
-2
-1
1
2
3
4
-10 -8 -6 -4 -2
-2
5 x
2
4
6
8 10 x
-4
-4
-6
-8
-8
-12
-10
-16
-20
Use the shape of the graph to name the function.
48)
y
Determine whether the given function is even, odd, or neither.
42) f(x) = x3 - 5x
43) f(x) = 4x2 + x4
x
44) f(x) = x3 - x2
Use possible symmetry to determine whether the graph is the
graph of an even function, an odd function, or a function that
is neither even nor odd.
45)
y
10
49)
8
y
6
4
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10 x
-4
-6
x
-8
-10
46)
y
10
8
6
4
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10 x
-4
-6
-8
-10
5
Begin by graphing the standard quadratic function f(x) = x 2 .
Then use transformations of this graph to graph the given
function.
53) h(x) = -(x + 2)2
50)
y
10
y
8
6
x
4
2
-10 -8 -6 -4 -2
-2
-4
2 4
6 8 10 x
-6
-8
-10
Begin by graphing the standard quadratic function f(x) = x 2 .
Then use transformations of this graph to graph the given
function.
51) g(x) = x2 - 2
Use the graph of y = f(x) to graph the given function g.
54) g(x) = 2f(x)
y
y
6
12
10
8
4
2
6
4
10
8
2
-10 -8 -6 -4 -2-2
2
4 6
8 10 x
-12 -10 -8 -6 -4 -2
-2
-4
-6
-4
-6
-8
2
4 6 8 10 12
x
-8
-10
-10
-12
Use the graph of the function f, plotted with a solid line, to
sketch the graph of the given function g.
52) g(x) = x - 3
10
Begin by graphing the standard quadratic function f(x) = x 2 .
Then use transformations of this graph to graph the given
function.
55) h(x) = (x - 6)2 + 2
y
8
6
4
2
-10 -8 -6 -4 -2
-2
-4
10
2 4 6
y
8
6
8 10 x
4
2
-6
-8
-10 -8 -6 -4 -2
-2
-4
-10
2 4
-6
-8
-10
Find the domain of the function.
56) f(x) = 5x + 6
6
6 8 10 x
57) f(x) = 58) h(x) = 59)
72) f(x) = x; x
2
x + 18
Determine which two functions are inverses of each other.
x
3
73) f(x) = 3x
g(x) = h(x) = 3
x
x - 1
x3 - 4x
x
x - 6
60) f(x) = g(x) = 2x + 4
74) f(x) = x - 3
2
75) f(x) = x3 - 3
1
4
+ x - 5 x + 8
77) f(x) = 62) f(x) = 5x2 - 7x, g(x) = x2 - 2x - 35
f
Find .
g
g(x) = -2x + 8
64) f(x) = 3x + 5,
Find fg.
g(x) = 6x - 6
h(x) = 3
g(x) = x - 3
h(x) = x3 + 3
Find the inverse of the one-to-one function.
76) f(x) = 8x + 4
Given functions f and g, perform the indicated operations.
61) f(x) = 7x - 5,
g(x) = 2x - 4
Find f - g.
63) f(x) = 6 - 8x,
Find f + g.
3
8x - 5
78) f(x) = x + 4
3
79) f(x) = x + 8
Does the graph represent a function that has an inverse
function?
80)
y
Given functions f and g, determine the domain of f + g.
4
65) f(x) = 4x - 1,
g(x) = x - 5
For the given functions f and g , find the indicated
composition.
66) f(x) = 12x2 - 9x, g(x) = 18x - 3
x
(f∘g)(8)
67) f(x) = 3x + 10,
(f∘g)(x)
g(x) = 3x - 1
7
,
68) f(x) = x + 1
4
g(x) = 5x
81)
y
(f∘g)(x)
69) f(x) = 4x 2 + 6x + 4,
(g∘f)(x)
g(x) = 6x - 5
x
Find the domain of the composite function f∘g.
70) f(x) = 4x + 28,
g(x) = x + 6
71) f(x) = x + 1,
g(x) = x + 3
2
g(x) = 2x - 3
4
x + 6
7
Graph f as a solid line and f-1 as a dashed line in the same
rectangular coordinate space. Use interval notation to give the
domain and range of f and f-1 .
82)
y
85) f(x) = x2 - 8, x ≥ 0
10
x
y
8
6
4
2
-10 -8
-6
-4
-2
2
4
6
8
x
2
4
6
8
x
2
4
6
8
x
-2
Use the graph of f to draw the graph of its inverse function.
83)
-4
-6
y
-8
10
-10
5
86) f(x) = (x + 1)3
-10
-5
5
10
x
10
-5
y
8
6
-10
4
2
84)
-10 -8
-6
-4
-2
-2
y
-4
10
-6
5
-8
-10
-10
-5
5
10
x
87) f(x) = x - 4
-5
10
-10
y
8
6
4
2
-10 -8
-6
-4
-2
-2
-4
-6
-8
-10
8
Write the standard form of the equation of the circle with the
given center and radius.
88) (7, 8); 9
89) (0, 2); 11
90) (0, 3); 2
91) (0, 0); 10
Find the center and the radius of the circle.
92) (x + 7)2 + (y + 8)2 = 49
Graph the equation.
93) (x - 5)2 + (y - 3)2 = 9
10
y
5
-10
-5
5
10 x
-5
-10
Complete the square and write the equation in standard form.
Then give the center and radius of the circle.
94) x2 + 6x + 9 + y 2 + 16y + 64 = 64
95) x2 + y 2 - 2x + 6y = -6
96) x2 + y2 - 6x + 6y + 8 = 0
Graph the equation.
97) x2 + y 2 - 4x - 6y + 9 = 0
10
y
5
-10
-5
5
10 x
-5
-10
9
Answer Key
Testname: MTH 112 BTZ PRACTICE PROBLEMS (CH. 1)
1) domain = {4, 8, 7}; range = {-1, -7,
2, 6}
2) domain = {9, 4, -6, -7}; range = {8,
5, -4, -5}
3) domain: {-1, 7, -2, 23}; range: {-4,
-3, 0, 3, 5}
4) Function
5) Not a function
6) Function
7) y is a function of x
8) y is not a function of x
9) y is not a function of x
10) y is not a function of x
11) y is not a function of x
12) 5x2 - 8x + 6
13) 6
14) 3
15) - 3
11
16)
6
y
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
1
2
3
4
5
-2
-3
-4
-5
-6
g shifts the graph of f vertically up
3 units
17)
6
y
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
1
2
3
4
-2
-3
-4
-5
-6
g shifts the graph of f vertically
down 2 units
5
51)
18)
6
y
10
8
5
3
6
4
2
2
4
1
-6 -5 -4 -3 -2 -1
-1
-10 -8 -6 -4 -2-2
1
2
3
4
5
6
-4
2 4
6 8 10 x
2 4
6 8 10 x
52)
-6
g shifts the graph of f vertically
down 1 units
19) function
20) not a function
21) function
22) not a function
23) -3.4
24) 4
25) domain: (-∞, ∞)
range: (-∞, ∞)
26) domain: (-∞, ∞)
range: (-∞, 3]
27) domain: [0, ∞)
range: [-2, ∞)
28) (6, 0), (-6, 0), (0, 7), (0, -7)
29) (-2, 0), (0, 8)
30) (3, 0), (-3, 0), (0, -3)
31) 7(2x+h)
32) 2x + h + 9
33) 7
34) 6
35) 5
36) (0, 5)
37) (-1, 1)
38) (5, 12)
39) f has a relative maximum at x = 0;
the relative maximum is 3
40) maximum: (0, 1); minimum: (2, -3)
41) minimum: (2, -14); maximum: (-2,
18)
42) Odd
43) Even
44) Neither
45) Even
46) Neither
47) Odd
48) Standard cubic function
49) Square root function
50) Absolute value function
6 8 10 x
-8
-10
-3
-5
2 4
-4
-6
-2
10
y
10
y
8
6
4
2
-10 -8 -6 -4 -2-2
-4
-6
-8
-10
53)
10
y
8
6
4
2
-10 -8 -6 -4 -2
-2
-4
-6
-8
-10
54)
14
12
y
10
8
6
4
2
-12 -10 -8 -6 -4 -2
-2
-4
-6
-8
-10
-12
-14
2 4 6
8 10 1
Answer Key
Testname: MTH 112 BTZ PRACTICE PROBLEMS (CH. 1)
55)
86)
83)
10
y
y
8
6
10
4
5
10
8
6
2
-10 -8 -6 -4 -2
-2
-4
4
2
4 6
2
8 10 x
-10
-5
5
10
x
-10 -8
-6
-6
-4
-2
77) f-1 (x) = 80) Yes
81) No
82) No
8
-8
-10
y
f domain = (-∞, ∞); range = (-∞, ∞)
f-1 domain = (-∞, ∞); range = (-∞,
10
∞)
5
87)
10
-10
-5
5
10
x
y
8
6
-5
4
-10
2
85)
-10 -8
-6
-4
-2
2
4
6
8
-2
10
y
-4
8
-6
6
-8
4
-10
2
-10 -8
-6
-4
-2
2
4
6
8
-2
-4
3
5
+ 8x 8
78) f-1 (x) = x2 - 4
79) f-1 (x) = x3 - 8
6
-6
84)
63) -10x + 14
64) 18x2 + 12x - 30
69) 24x2 + 36x + 19
70) (-∞, ∞)
71) (-∞, -6) ∪ (-6, ∞)
72) [-2, ∞)
73) f(x) and g(x)
74) g(x) and h(x)
75) g(x) and h(x)
x - 4
76) f-1 (x) = 8
4
-4
-10
56) (-∞, ∞)
57) (-∞, ∞)
58) (-∞, -2) ∪ (-2, 0) ∪ (0, 2) ∪ (2, ∞)
59) (6, ∞)
60) (-∞, -8) ∪ (-8, 5) ∪ (5, ∞)
61) 5x - 1
5x2 - 7x
62)
x2 - 2x - 35
2
-2
-5
-8
-10
65) (-∞, 5) ∪ (5, ∞)
66) 237,303
67) 9x + 7
35x
68)
4 + 5x
y
-6
-8
-10
f domain = (0, ∞); range = (-8, ∞)
f-1 domain = (0, ∞); range = (-8, ∞)
f domain = (0, ∞); range = (4, ∞)
f-1 domain = (4, ∞); range = (0, ∞)
88) (x - 7)2 + (y - 8)2 = 81
89) x2 + (y - 2)2 = 121
90) x2 + (y - 3)2 = 2
91) x2 + y2 = 10
92) (-7, -8), r = 7
93)
10
y
5
-10
-5
5
10 x
-5
-10
Domain = (2, 8), Range = (0, 6)
11
Answer Key
Testname: MTH 112 BTZ PRACTICE PROBLEMS (CH. 1)
94) (x + 3)2 + (x + 8)2 = 64
(-3, -8), r = 8
95) (x - 1)2 + (x + 3)2 = 4
(1, -3), r = 2
96) (x - 3)2 +(y + 3)2 = 10
(3, -3), r = 10
97)
10
y
5
-10
-5
5
10 x
-5
-10
12