MTH 112 Practice Test #1 Sections P.9, 1.2, 1.3, 1.6, and 1.7
Graph the interval on a number line.
1) [-9, 3)
10) 5 + 1 - -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
x
≥ 8
2
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Use graphs to find the set.
2) (-∞, 3) ∩ [-8, 14)
Give the domain and range of the relation.
11) {(5, 8), (5, -1), (-12, 5), (-1, 6), (-9, 1)}
3) (-∞, 3) ∪ [-3, 13)
Determine whether the relation is a function.
12) {(1, -9), (1, -8), (6, -1), (9, 8), (11, 9)}
4) (-8, 0) ∪ [-4, 7]
13) {(-7, -2), (-4, -4), (1, -2), (3, -7)}
Solve the linear inequality. Use interval notation to
express the solution set and graph the solution set on a
number line.
5) 2x + 7 < 19
Determine whether the equation defines y as a function
of x.
14) 6x + 3y = 2
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
15) x2 + y2 = 4
6) -36x - 36 ≤ -6(5x + 9)
16) y = - x + 7
Evaluate the function at the given value of the
independent variable and simplify.
17) h(x) = x - 13 ; h(19)
Solve the compound inequality. Use interval notation to
express the solution set and graph the solution set on a
number line.
7) 12 ≤ 2x + 4 ≤ 18
18) f(x) = x2 + 5
;
x3 - 3x
19) g(x) = 4x + 2;
Solve the absolute value inequality. Use interval notation
to express the solution set and graph the solution set on a
number line.
8) |x - 2| < 5
f(-5)
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.
20)
y
-4
-2
0
2
4
6
8
10
12
14
16
-6
-4
-2
0
2
4
6
8
9) |x + 6| ≥ 0
-12 -10
-8
x
1
21)
Use the graph to determine the functionʹs domain and
range.
24)
y
6
y
5
4
3
x
2
1
-6 -5 -4 -3 -2 -1
-1
1
2
3
4
5
6 x
1
2
3
4
5
6 x
-2
-3
-4
-5
22)
-6
y
25)
6
y
5
x
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
-2
Use the graph to find the indicated function value.
23) y = f(x). Find f(-4), and f(0).
-3
-4
-5
5
y
-6
4
3
Identify the x-intercepts and y-intercepts.
26)
2
1
y
-5
-4
-3
-2
-1
1
2
3
4
5 x
10
-1
-2
5
-3
-4
-10
-5
-5
5
-5
-10
2
10
x
Find and simplify the difference quotient
f(x + h) - f(x)
, h≠ 0 for the given function.
h
The graph of a function f is given. Use the graph to
answer the question.
31) Find the numbers, if any, at which f has a
relative maximum. What are the relative
maxima?
27) f(x) = x2 + 6x + 3
5
28) f(x) = 6x + 3
y
4
3
Evaluate the piecewise function at the given value of the
independent variable.
29)
-3x - 5 if x < -1
f(x) =
2x + 4 if x ≥ -1
2
1
-5
-4
-3
-2
-1
1
2
3
4
5 x
-1
-2
-3
Determine f(-4), f(-1), and f(10).
-4
-5
Identify the intervals where the function is increasing,
decreasing, and constant.
30) Increasing
4
32) Find the numbers, if any, at which f has a
relative minimum. What are the relative
minima?
3
5
2
4
1
3
5
-5
-4
-3
-2
-1
y
1
2
3
4
y
2
5 x
-1
1
-2
-5
-3
-4
-3
-2
-1
1
2
3
4
5 x
-1
-4
-2
-5
-3
-4
-5
Determine whether the given function is even, odd, or
neither.
33) f(x) = x3 - 5x
34) f(x) = 3x2 + x4
35) f(x) = x3 + x2 + 4
3
39)
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 be matched. Use your book to learn
all 7.
36)
y
y
x
x
40)
y
37)
y
x
x
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.
41)
38)
y
10
y
8
6
4
2
-10 -8 -6 -4 -2
-2
-4
x
-6
-8
-10
4
2
4
6
8 10 x
42)
Begin by graphing the standard absolute value function
f(x) = x . Then use transformations of this graph to graph
the given function.
45) g(x) = x + 3
y
10
8
6
4
10
2
-10 -8 -6 -4 -2
-2
2
4
6
y
8
6
4
2
8 10 x
-4
-6
-8
-10 -8 -6 -4 -2-2
-4
-10
2 4
6 8 10 x
-6
-8
-10
43)
y
10
Begin by graphing the standard quadratic function
f(x) = x 2 . Then use transformations of this graph to graph
8
6
4
the given function with a dotted graph.
46) h(x) = (x - 2)2
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10 x
-4
10
-6
8
6
-8
y
4
2
-10
-10 -8 -6 -4 -2
-2
-4
Begin by graphing the standard quadratic function f(x) =
x 2 . Then use transformations of this graph to graph the
2 4
6 8 10 x
-6
-8
given function.
44) g(x) = x2 - 2
-10
10
y
Begin by graphing the standard square root function
f(x) = x . Then use transformations of this graph to
graph the given function with a dotted graph
47) h(x) = x + 2
8
6
4
2
-10 -8 -6 -4 -2
-2
2
4
6 8 10 x
10
8
-4
-6
y
6
4
-8
-10
2
-10 -8 -6 -4 -2-2
-4
-6
-8
-10
5
2 4
6 8 10 x
51) g(x) = 2f(x)
Begin by graphing the standard quadratic function f(x) =
x 2 . Then use transformations of this graph to graph the
given function with a dotted graph.
48) h(x) = -(x + 2)2
10
8
y
12
10
8
6
4
y
6
4
2
2
-12 -10 -8 -6 -4 -2
-2
-4
-6
-10 -8 -6 -4 -2-2
2
4
6 8 10 x
-4
-6
-8
-10
-8
-12
2
4 6 8 10 12
x
-10
Begin by graphing the square root function f(x) = x
Then use transformations of this graph to graph the given
function as a dotted graph.
52) g(x) = 4 x + 2
Begin by graphing the standard absolute value function
f(x) = x . Then use transformations of this graph to graph
the given function with a dotted graph.
49) h(x) = - x + 2
10
y
10
8
6
8
6
4
2
4
-10 -8 -6 -4 -2
-2
-4
2
4
2
6 8 10 x
-10 -8
-6
-4
-2
2
-2
-6
-8
-4
-10
-6
-8
Use the graph of the function f, plotted as a solid graph, to
sketch the graph of the given function g with a dotted
graph.
50) g(x) = - f(x) + 2
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
y
-10
y
y = f(x)
1 2 3 4 5 6 x
6
4
6
8
x
Begin by graphing the standard absolute value function
f(x) = x . Then use transformations of this graph to graph
the given function as a dotted graph.
1
53) g(x) = x - 6 - 2
2
Given functions f and g, determine the domain of f + g.
4
60) f(x) = 4x - 1,
g(x) = x - 5
61) f(x) = 3x
,
x - 1
g(x) = 5
x + 9
y
10
8
6
Find the domain of the indicated combined function.
62) Find the domain of (f - g)(x) when f(x) = 6x - 7
and g(x) = 3x - 9.
4
2
-10 -8 -6 -4 -2-2
2 4
6 8 10 x
63) Find the domain of -4
-6
and g(x) = x2 - 4x - 2.
-8
-10
For the given functions f and g , find the indicated
composition.
64) f(x) = 3x + 10, g(x) = 3x - 1
(f∘g)(x)
Use the graph of the function f, plotted with a solid line,
to sketch the graph of the given function g (dotted).
54) g(x) = f(x - 1) + 2
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
65) f(x) = 12x2 - 9x, g(x) = 18x - 3
(f∘g)(8)
y
y = f(x)
66) f(x) = g(x) = 4
5x
Find the domain of the composite function f∘g.
5
67) f(x) = ,
g(x) = x + 5
x + 7
68) f(x) = x; x
x2 - 16
57) f(x) = 19 - x
Given functions f and g, perform the indicated
operations.
58) f(x) = 7x - 5,
g(x) = 2x - 4
Find f - g.
59) f(x) = 3x + 5,
Find fg.
7
,
x + 1
(f∘g)(x)
1 2 3 4 5 6 x
Find the domain of the function.
55) f(x) = x2 + 8
56) g(x) = f
(x) when f(x) = 8x2 - 4x
g
g(x) = 6x - 6
7
g(x) = 2x + 4
Answer Key
Testname: 112PRACTICETEST1
1)
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
2)
3)
4)
5)
[-8, 3)
(-∞, 13)
(-8, 7]
(-∞, 6)
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
6) [3, ∞)
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
7) [4, 7]
-1
0
1
2
3
4
-2
0
2
4
-8
-6
-4
5
6
7
8
9
10 11 12
6
8
10
12
14
16
18
20
-2
0
2
4
6
8
10
12
8) (-3, 7)
-4
9) (-∞, ∞)
-12
-10
10) (-∞, -4] ∪ [8, ∞)
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
11) domain = {-1, 5, -12, -9}; range = {6, -1, 5, 1, 8}
12) Not a function
13) Function
14) y is a function of x
15) y is not a function of x
16) y is a function of x
17) 6
3
18) - 11
19) 4x + 6
20) not a function
21) not a function
22) function
23) 4, 0
24) domain: (-∞, ∞)
range: [-4, ∞)
25) domain: [0, ∞)
range: [-3, ∞)
26) x-intercepts: (6, 0), (-6, 0)
y-intercepts: (0, 7), (0, -7)
27) 2x + h + 6
8
Answer Key
Testname: 112PRACTICETEST1
28) 6
29) 7, 2, 24
30) inc: (0, 3)
dec: (-1, 0)
constant: (-∞, -1), (3, ∞)
31) f has a relative maximum at x = 0; the relative maximum is 2
32) f has a relative minimum at x = -2 and 2; the relative minimum is 0
33) Odd
34) Even
35) Neither
36) Absolute value function
37) Standard cubic function
38) Standard quadratic function
39) Identity function
40) Square root function
41) Odd
42) Neither
43) Even
44)
10
8
y
6
4
2
-10 -8 -6 -4 -2-2
2
4
6 8 10 x
2
4
6 8 10 x
-4
-6
-8
-10
45)
10
8
y
6
4
2
-10 -8 -6 -4 -2-2
-4
-6
-8
-10
9
Answer Key
Testname: 112PRACTICETEST1
46)
10
8
y
6
4
2
-10 -8 -6 -4 -2-2
2
4
6 8 10 x
2
4
6 8 10 x
2
4
6 8 10 x
2
4
6 8 10 x
-4
-6
-8
-10
47)
10
8
y
6
4
2
-10 -8 -6 -4 -2-2
-4
-6
-8
-10
48)
10
y
8
6
4
2
-10 -8 -6 -4 -2
-2
-4
-6
-8
-10
49)
10
y
8
6
4
2
-10 -8 -6 -4 -2
-2
-4
-6
-8
-10
10
Answer Key
Testname: 112PRACTICETEST1
50)
6
5
4
3
2
1
y
1 2 3 4 5 6 x
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
51)
14
y
12
10
8
6
4
2
-12 -10 -8 -6 -4 -2
-2
-4
-6
2 4
6 8 10 12
x
-8
-10
-12
-14
52)
10
y
8
6
4
2
-10 -8
-6
-4
-2
2
4
6
8
x
-2
-4
-6
-8
-10
11
Answer Key
Testname: 112PRACTICETEST1
53)
10
8
y
6
4
2
-10 -8 -6 -4 -2-2
2
4
6 8 10 x
-4
-6
-8
-10
54)
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
y
1 2 3 4 5 6 x
55) (-∞, ∞)
56) (-∞, -4) ∪ (-4, 4) ∪ (4, ∞)
57) (-∞, 19]
58) 5x - 1
59) 18x2 + 12x - 30
60) (-∞, 5) ∪ (5, ∞)
61) (-∞, -9) ∪ (-9, 1) ∪ (1, ∞)
62) Domain: (-∞, ∞)
63) Domain: -∞, 2 - 6 ∪ 2 - 6, 2 + 6 ∪ 2 + 6, ∞
64) 9x + 7
65) 237,303
35x
66)
4 + 5x
67) (-∞, -12) ∪ (-12, ∞)
68) [-2, ∞)
12