MTH 112 Practice Test 1
Sections 1.2, 1.3, 1.6, 1.7, 1.9, 2.8
Give the domain and range of the relation.
1) {(5, 8), (5, -1), (-12, 5), (-1, 6), (-9, 1)}
12)
y
Determine whether the relation is a function.
2) {(1, -9), (1, -8), (6, -1), (9, 8), (11, 9)}
3) {(-7, -2), (-4, -4), (1, -2), (3, -7)}
x
Determine whether the equation defines y as a function of
x.
4) 6x + 3y = 2
5) x2 + y2 = 4
13)
y
6) y = - x + 7
7) x2 + y = 9
Evaluate the function at the given value of the
independent variable and simplify.
8) h(x) = x - 13 ; h(19)
9) f(x) =
x2 + 5
;
x3 - 3x
10) g(x) = 4x + 2;
x
f(-5)
Use the graph to find the indicated function value.
14) y = f(x). Find
(a) f(5) (b) f(-3) (c) x when f(x)=4
g(x + 1)
Use the vertical line test to determine whether or not the
graph is a graph in which y is a function of x.
11)
5
y
4
3
y
2
1
-5
-4
-3
-2
-1
1
-1
-2
x
-3
-4
-5
1
2
3
4
5 x
Use the graph to determine the function's domain and
range.
15)
6
Find and simplify the difference quotient
f(x + h) - f(x)
, h≠ 0 for the given function.
h
y
18) f(x) = x2 + 9x - 8
5
4
19) f(x) = 7x2
3
2
Evaluate the piecewise function at the given value of the
independent variable.
20)
-3x - 5 if x < -1
f(x) =
2x + 4 if x ≥ -1
1
-6 -5 -4 -3 -2 -1
-1
1
2
3
4
5
6 x
-2
-3
-4
-5
-6
Determine f(-4), f(-1), f(10).
Identify the intervals where the function is indreasing,
decreasing, and constant.
21)
16)
6
y
5
5
4
4
3
3
2
y
2
1
1
-6 -5 -4 -3 -2 -1
-1
1
2
3
4
5
6 x
-5
-2
-4
-3
-2
-1
1
-1
-3
-2
-4
-5
-3
-6
-4
-5
Identify the intercepts.
17)
y
10
5
-10
-5
5
10
x
-5
-10
2
2
3
4
5 x
The graph of a function f is given. Use the graph to answer
the question.
22) Find the numbers, if any, at which f has a
relative maximum. What are the relative
maxima?
5
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.
27)
y
10
y
8
4
6
3
4
2
2
1
-5
-4
-3
-2
-10 -8 -6 -4 -2
-2
-1
1
2
3
4
2
4
6
8 10 x
2
4
6
8 10 x
2
4
6
8 10 x
-4
5 x
-6
-1
-8
-2
-10
-3
-4
28)
-5
y
10
Use the graph of the given function to find any relative
maxima and relative minima.
23) f(x) = x3 - 3x2 + 1
5
8
6
4
2
y
4
-10 -8 -6 -4 -2
-2
3
-4
2
-6
-8
1
-5
-4
-3
-2
-1
-10
1
2
3
4
5 x
-1
29)
-2
y
-3
10
-4
8
-5
6
4
2
Determine whether the given function is even, odd, or
neither.
24) f(x) = x3 + 4
-10 -8 -6 -4 -2
-2
-4
-6
-8
-10
25) f(x) = 4x2 + x4
26) f(x) = x3 - 5x
3
Use the shape of the graph to name the function. On the
test, this will be matching. The graph, its name, and its
equation will have to be matched.
30)
33)
y
y
x
x
34)
y
31)
y
x
x
35)
y
32)
y
x
x
36)
y
x
4
Use transformations of this graph to graph the given
function.
37) g(x) = x - 1
40) g(x) = -
x-1
10
10
y
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2-2
y
2
4
-10 -8 -6 -4 -2
-2
-4
6 8 10 x
-4
-6
-6
-8
-8
-10
2 4
6
8 10 x
-10
41) g(x) = 4 x + 2
38) g(x) = x + 3
y
10
10
y
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2-2
2
4
-12 -10 -8 -6 -4 -2-2
6 8 10 x
2
4 6
8 10
x
-4
-4
-6
-6
-8
-8
-10
-10
Use the graph of the function f, plotted with a solid line, to
sketch the graph of the given function g.
42) g(x) = f(x + 2)
1
39) g(x) = - x3
4
10
8
6
5
4
3
2
1
y
6
4
2
-10 -8 -6 -4 -2-2
2
4
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
6 8 10 x
-4
-6
-8
-10
5
y
y = f(x)
1 2 3 4 5 6 x
43) g(x) = -f(x + 2) - 1
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
51) f(x) = 4x - 1,
g(x) =
4
x-5
y
Find the domain of the indicated combined function.
52) Find the domain of (f - g)(x) when f(x) = 6x - 7
and g(x) = 3x - 9.
y = f(x)
1 2 3 4 5 6 x
53) Find the domain of
f
(x) when f(x) = 3x2 - 2x
g
and g(x) = x2 + 5x + 4.
For the given functions f and g , find the indicated
composition.
54) f(x) = 12x2 - 9x, g(x) = 18x - 3
Use the graph of y = f(x) to graph the given function g.
44) g(x) = 2f(x)
(f∘g)(8)
y
55) f(x) = -4x + 3,
(g∘f)(x)
12
10
g(x) = 6x + 4
8
6
4
56) f(x) =
2
-12 -10 -8 -6 -4 -2
-2
-4
4 6
57) f(x) = x2 + 2x - 4,
(f∘g)(2)
Find the domain of the function.
45) f(x) = x2 + 8
19 - x
g(x) = x2 + 2x + 5
Find the domain of the composite function f∘g.
5
58) f(x) =
,
g(x) = x + 5
x+7
-12
47) f(x) =
4
5x
8 10 12 x
-8
-10
x
2
x - 16
g(x) =
(f∘g)(x)
2
-6
46) g(x) =
7
,
x+1
59) f(x) =
2x - 1 ; g(x) = 3x
Find the coordinates of the vertex for the parabola defined
by the given quadratic function.
60) f(x) = -x2 + 2x + 5
61) f(x) = -3x2 + 6x - 6
Given functions f and g, perform the indicated operations.
48) f(x) = 7x - 5,
g(x) = 2x - 4
Find f - g.
49) f(x) = 3x + 5,
Find fg.
62) f(x) = -7(x - 5)2 - 8
63) f(x) = x2 + 6
g(x) = 6x - 6
Find the axis of symmetry of the parabola defined by the
given quadratic function.
64) f(x) = 11(x - 3)2 + 4
Given functions f and g, determine the domain of f + g.
3x
5
50) f(x) =
,
g(x) =
x-1
x+9
6
65) f(x) = 6x2 + 12x + 2
72) f(x) = x2 + 6x + 5
y
10
Find the range of the quadratic function.
66) f(x) = 2x2 - 2x + 2
5
67) f(x) = (x + 3)2 + 9
-10
-5
Find the x-intercepts (if any) for the graph of the quadratic
function.
68) f(x) = 4 + 5x + x2
x
-10
Determine whether the given quadratic function has a
minimum value or maximum value. Then find the
coordinates of the minimum or maximum point.
73) f(x) = -x2 - 3x - 8
Find the domain and range of the quadratic function
whose graph is described.
70) The vertex is (1, -6) and the graph opens
down.
74) f(x) = 3x2 - 2x + 1
Solve the problem.
75) The profit that the vendor makes per day by
selling x pretzels is given by the function
P(x) = -0.002x2 + 1.6x - 100.
Use the vertex and intercepts to sketch the graph of the
quadratic function.
71) f(x) = 8 - x2 - 2x
A)Find the number of pretzels that must be
sold to maximize profit.
B) What is the maximum profit?
y
10
76) You have 344 feet of fencing to enclose a
rectangular region. What is the maximum
area?
5
-5
10
-5
Find the y-intercept for the graph of the quadratic
function.
69) f(x) = 3x2 - 5x - 8
-10
5
5
10
x
Determine whether the function is a polynomial function.
2
77) f(x) = 9 x4
-5
-10
A) No
7
B) Yes
78) f(x) = x3/2 - x6 + 3
A) No
B) Yes
79) f(x) = 3x + 2x3
A) No
B) Yes
4
80) f(x) = x5 - x3 - 8
A) No
B) Yes
Determine whether the graph shown is the graph of a
polynomial function.
81)
Determine whether the graph of the polynomial has y-axis
symmetry, origin symmetry, or neither.
87) f(x) = 8 - x4
A) origin symmetry
B) y-axis symmetry
C) neither
y
88) f(x) = 7x2 - x3
A) y-axis symmetry
B) origin symmetry
C) neither
x
89) x5 - 28x3 + 75x = 0
A) y-axis symmetry
B) origin symmetry
C) neither
A) not a polynomial function
B) polynomial function
82)
90)
y
y
6
5
4
3
2
1
x
1 2 3 4 5 6 x
-6 -5 -4 -3 -2 -1-1
-2
-3
-4
-5
-6
A) not a polynomial function
B) polynomial function
A) origin symmetry
B) y-axis symmetry
C) neither
Find the x-intercepts of the polynomial function. State
whether the graph crosses the x-axis, or touches the x-axis
and turns around, at each intercept.
83) f(x) = 7x2 - x3
91)
y
6
5
4
3
2
1
84) f(x) = (x + 1)(x - 9)(x - 1)2
Find the y-intercept of the polynomial function.
85) f(x) = -x2 + 2x + 3
-6 -5 -4 -3 -2 -1-1
-2
-3
-4
-5
-6
86) f(x) = (x + 1)(x - 4)(x - 1)2
1 2 3 4 5 6 x
A) y-axis symmetry
B) origin symmetry
C) neither
8
92)
98) f(x) = 5(x2 + 1)(x + 4)2
y
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1-1
-2
-3
-4
-5
-6
Use the Intermediate Value Theorem to determine
whether the polynomial function has a real zero between
the given integers.
99) f(x) = 9x3 - 6x2 + 2x - 7; between 1 and 2
1 2 3 4 5 6 x
100) f(x) = 2x4 - 5x2 - 6; between 1 and 2
Graph the polynomial function.
101) f(x) = 2x2 - x3
y
A) y-axis symmetry
B) origin symmetry
C) neither
10
Use the Leading Coefficient Test to determine the end
behavior of the polynomial function. Then use this end
behavior to match the function with its graph.
93) f(x) = 6x3 + 2x2 - 3x + 1
5
-10
-5
A) rises to the left and rises to the right
B) rises to the left and falls to the right
C) falls to the left and rises to the right
D) falls to the left and falls to the right
5
10
x
-5
-10
94) f(x) = 5x4 - 2x2
A) rises to the left and rises to the right
B) rises to the left and falls to the right
C) falls to the left and rises to the right
D) falls to the left and falls to the right
102) f(x) = x4 - 4x2
12
y
10
Use the Leading Coefficient Test to determine the end
behavior of the polynomial function.
95) f(x) = -3x3 - 3x2 - 2x + 1
8
6
4
A) falls to the left and rises to the right
B) rises to the left and rises to the right
C) rises to the left and falls to the right
D) falls to the left and falls to the right
2
-12 -10 -8 -6 -4 -2
-2
-4
-6
Find the zeros of the polynomial function.
96) f(x) = x3 + 8x2 - x - 8
-8
-10
-12
Find the zeros for the polynomial function and give the
multiplicity for each zero. State whether the graph crosses
the x-axis or touches the x-axis and turns around, at each
zero.
97) f(x) = 4(x - 4)(x + 3)3
9
2
4
6 8 10 12 x
Answer Key
Testname: MTH 112 PRACTICETEST1
1)
2)
3)
4)
5)
6)
7)
8)
domain = {-1, 5, -12, -9}; range = {6, -1, 5, 1, 8}
Not a function
Function
y is a function of x
y is not a function of x
y is a function of x
y is a function of x
6
3
9) 11
37)
10
y
8
6
4
2
-10 -8 -6 -4 -2-2
-4
2 4
6
8 10 x
2 4
6
8 10 x
2 4
6
8 10 x
2 4
6
8 10 x
-6
-8
10) 4x + 6
11) not a function
12) function
13) not a function
14) 2, 3, -4
15) domain: (-∞, ∞)
range: [-4, ∞)
16) domain: [0, ∞)
range: [-2, ∞)
17) (6, 0), (-6, 0), (0, 7), (0, -7)
18) 2x + h + 9
19) 7(2x+h)
20) 7, 2, 24
21) (-2, 2), (-3,-2), (-∞,-3) & (2,∞)
22) f has a relative maximum at x = 0; the relative
maximum is 3
23) maximum: (0, 1); minimum: (2, -3)
24) Neither
25) Even
26) Odd
27) Odd
28) Even
29) Neither
30) Standard cubic function y=x3
-10
38)
10
y
8
6
4
2
-10 -8 -6 -4 -2-2
-4
-6
-8
-10
39)
10
8
y
6
4
2
-10 -8 -6 -4 -2-2
-4
-6
-8
31) Square root function, y= x
-10
32) Standard quadratic function, y=x2
33) Absolute value function, y= x
34) Identity function, y=x
3
35) Cube Root function, y= x
1
36) Reciprocal function, y=
x
40)
10
y
8
6
4
2
-10 -8 -6 -4 -2-2
-4
-6
-8
-10
10
Answer Key
Testname: MTH 112 PRACTICETEST1
41)
44)
10
y
14
8
-10 -8
-6
-4
6
10
8
4
6
2
4
2
-2
2
4
6
8
x
-2
-12 -10 -8 -6 -4 -2-2
-4
-4
-6
-6
-8
-8
-10
-12
-10
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
6
8 10 12
45) (-∞, ∞)
46) (-∞, -4) ∪ (-4, 4) ∪ (4, ∞)
47) (-∞, 19]
48) 5x - 1
49) 18x2 + 12x - 30
y
50) (-∞, -9) ∪ (-9, 1) ∪ (1, ∞)
51) (-∞, 5) ∪ (5, ∞)
52) Domain: (-∞, ∞)
53) Domain: -∞, -4 u -4, -1 u -1, ∞
54) 237,303
55) -24x + 22
35x
56)
4 + 5x
1 2 3 4 5 6 x
43)
6
5
4
3
2
1
2 4
-14
42)
6
5
4
3
2
1
y
12
y
57) 191
58) (-∞, -12) ∪ (-12, ∞)
1
59) [ , ∞)
6
60) (1, 6)
61) (1, -3)
62) (5, -8)
63) (0, 6)
64) x = 3
65) x = -1
3
66) [ , ∞)
2
1 2 3 4 5 6 x
67) [9, ∞)
68) (-1, 0) and (-4, 0)
69) (0, -8)
70) Domain: (-∞, ∞)
Range: (-∞, -6]
11
x
Answer Key
Testname: MTH 112 PRACTICETEST1
71)
90) B
91) C
92) B
93) C
94) A
95) C
96) x = -1, x = 1, x = - 8
97) 4, multiplicity 1, crosses x-axis; -3, multiplicity 3,
crosses x-axis
98) -4, multiplicity 2, touches the x-axis and turns
around
99) f(1) = -2 and f(2) = 45; yes
100) f(1) = -9 and f(2) = 6; yes
101)
y
10
5
-10
-5
5
10
x
-5
-10
y
72)
10
y
10
5
5
-10
-10
-5
5
10
-5
5
x
10
x
8
x
-5
-5
-10
-10
73) maximum; -
102)
3
23
,2
4
20
y
16
1 2
74) minimum; ,
3 3
12
8
4
75) 400 pretzels, $220
76) 7396 square feet
77) A
78) A
79) B
80) A
81) A
82) B
83) 0, touches the x-axis and turns around;
7, crosses the x-axis
84) -1, crosses the x-axis;
9, crosses the x-axis;
1, touches the x-axis and turns around
85) 3
86) -4
87) B
88) C
89) B
-8
-6
-4
-2
-4
-8
-12
-16
-20
12
2
4
6