Practice Exam #1 (these are practice problems on sections covered for the test - problems on the exam will come from similar
problems to these, the homework and the quizzes)
Name___________________________________
10)
SHORT ANSWER. Write the word or phrase that best
completes each statement or answers the question.
y
Determine whether the relation is a function.
1) {(-6, 6), (-6, -6), (1, 3), (3, -8), (8, -6)}
2) {(-4, -7), (-1, -8), (1, -5), (7, 3)}
x
3) {(-3, -5), (3, -2), (5, 2), (7, -4), (11, 7)}
Determine whether the equation defines y as a function
of x.
4) x + y = 81
Use the graph to find the indicated function value.
11) y = f(x). Find f(-2)
5) x2 + y = 64
5
Evaluate the function at the given value of the
independent variable and simplify.
6) f(x) = 4x2 + 2x + 6; f(x - 1)
y
4
3
2
7) g(x) = 5x + 4;
g(x + 1)
1
-5
8) f(x) = x3 + 7
x2 + 5
-4
-3
-2
-1
1
2
3
4
5 x
1
2
3
4
5 x
-1
;
f(-1)
-2
-3
-4
Use the vertical line test to determine whether or not the
graph is a graph in which y is a function of x.
9)
-5
12) y = f(x). Find f(2)
y
y
12
10
8
6
x
4
2
-5
-4
-3
-2
-1 -2
-4
-6
-8
-10
-12
1
Use the graph to determine the functionʹs domain and
range.
13)
6
Identify the intervals where the function is changing as
requested.
16) Constant
y
5
5
4
4
3
3
y
2
2
1
1
-6 -5 -4 -3 -2 -1
-1
1
2
3
4
5
6 x
-5
-4
-3
-2
-1
1
2
3
4
5 x
1
2
3
4
5 x
2
4
6
8
10 x
-1
-2
-2
-3
-4
-3
-5
-4
-6
-5
17) Increasing
14)
5
6
y
y
4
5
3
4
2
3
1
2
1
-5
-6 -5 -4 -3 -2 -1
-1
1
2
3
4
5
-4
-3
-2
-1
-1
6 x
-2
-2
-3
-3
-4
-4
-5
-5
-6
18) Increasing
5
15)
10
4
y
3
8
2
6
1
4
2
-10 -8
-6
-4
-2
-1
-10 -8
-6
-4
-2
y
2
4
6
8
x
-2
-2
-3
-4
-4
-6
-5
-8
-10
2
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.
24)
The graph of a function f is given. Use the graph to
answer the question.
19) Find the numbers, if any, at which f has a
relative maximum. What are the relative
maxima?
5
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
-4
5 x
-6
-1
-8
-2
-10
-3
-4
25)
-5
y
10
Use the graph of the given function to find any relative
maxima and relative minima.
20) f(x) = x3 - 12x + 2
20
8
6
4
2
y
16
-10 -8 -6 -4 -2
-2
12
-4
8
-6
-8
4
-5
-4
-3
-2
-1
-10
1
2
3
4
5 x
-4
Graph the function.
26) f(x) = -x + 3
2x - 3
-8
-12
-16
if x < 2
if x ≥ 2
y
-20
5
Determine whether the given function is even, odd, or
neither.
21) f(x) = x3 - 3x
-5
5
22) f(x) = 5x2 + x4
-5
23) f(x) = x5 - x4
3
x
x + 5
27) f(x) = -4
-x + 5
if -8 ≤ x < 2
if x = 2
if x > 2
33) f(x) = x - y
Given functions f and g, perform the indicated
operations.
34) f(x) = 7x - 9,
g(x) = 2x - 4
Find f - g.
10
5
-10
4
x - 9
-5
5
10
x
35) f(x) = 9 - 6x,
Find f + g.
g(x) = -2x + 6
36) f(x) = 7x - 1,
Find fg.
g(x) = 9x - 4
-5
-10
Given functions f and g, determine the domain of f + g.
2
37) f(x) = 2x + 1,
g(x) = x + 4
Based on the graph, find the range of y = f(x).
4
if -5 ≤ x < -3
|x|
if -3 ≤ x < 5
28) f(x) = 3
x
if 5 ≤ x ≤ 12
10
Find the domain of the indicated combined function.
f
38) Find the domain of (x) when f(x) = 4x2 - 8x
g
y
and g(x) = x2 - 6x - 3.
(-3, 4)5
(-5, 4)
(-3, 3)
(5, 5)
For the given functions f and g , find the indicated
composition.
39) f(x) = 20x2 - 5x, g(x) = 14x - 3
(12, 2.3)
(5, 1.7)
-10
-5
5
10
15
x
(f∘g)(2)
-5
40) f(x) = 3x + 7,
(f∘g)(x)
-10
41) f(x) = 4x2 + 2x + 5,
(g∘f)(x)
Find and simplify the difference quotient
f(x + h) - f(x)
, h≠ 0 for the given function.
h
Find the domain of the function.
30) f(x) = x2 + 5
32)
g(x) = 2x - 4
Find the domain of the composite function f∘g.
g(x) = x + 3
42) f(x) = 4x + 40,
29) f(x) = 5x2
31) f(x) = g(x) = 2x - 1
43) f(x) = 4
,
x + 9
g(x) = 9
x
Find functions f and g so that h(x) = (f ∘ g)(x).
44) h(x) = |2x + 7|
x2
x2 + 6
45) h(x) = (6x - 14)8
x
x - 4
4
Determine which two functions are inverses of each other.
x - 6
x + 6
46) f(x) = g(x) = 4x - 6
h(x) = 4
4
52) g(x) = 2 x + 4
10
y
8
Find the inverse of the one-to-one function.
5
47) f(x) = 7x - 8
6
4
2
48) f(x) = x + 8
-10 -8
-6
-4
-2
2
4
10
y
6
x
8
-2
-4
49) f(x) = 4x + 5
-6
-8
Does the graph represent a function that has an inverse
function?
50)
-10
A)
y
8
6
4
2
x
-10 -8
-6
-4
-2
2
4
6
8
x
2
4
6
8
x
-2
-4
-6
-8
-10
51)
B)
y
10
y
8
6
4
2
x
-10 -8
-6
-4
-2
-2
-4
-6
-8
-10
MULTIPLE CHOICE. Choose the one alternative that
best completes the statement or answers the question.
Begin by graphing the square root function f(x) = x
Then use transformations of this graph to graph the given
function.
5
C)
A)
10
y
14
8
6
6
4
4
2
-10 -8
-6
-4
y
12
10
8
2
-2
2
4
6
8
x
-12 -10 -8 -6 -4 -2-2
-2
2 4
6 8 10 12 x
2 4
6 8 10 12 x
2 4
6 8 10 12 x
-4
-6
-8
-4
-6
-10
-12
-8
-10
-14
D)
B)
10
y
14
12
10
8
6
y
8
6
4
4
2
2
-10 -8
-6
-4
-2
2
4
6
8
x
-12 -10 -8 -6 -4 -2
-2
-4
-6
-2
-4
-6
-8
-10
-12
-8
-10
-14
C)
Use the graph of y = f(x) to graph the given function g.
53) g(x) = -2f(x)
14
12
10
8
6
y
12
10
8
4
2
6
4
-12 -10 -8 -6 -4 -2
-2
-4
2
-12 -10 -8 -6 -4 -2-2
y
2 4
6 8 10 12
-6
-8
-10
x
-4
-6
-12
-14
-8
-10
-12
6
D)
B)
14
y
10
8
12
10
8
6
4
6
4
2
2
-10 -8 -6 -4 -2-2
-12 -10 -8 -6 -4 -2-2
4 6
8 10 x
2
4 6
8 10 x
2
4 6
8 10 x
-8
-10
-8
-10
C)
-12
-14
10
y
8
6
4
Begin by graphing the standard quadratic function f(x) =
x 2 . Then use transformations of this graph to graph the
2
given function.
-10 -8 -6 -4 -2-2
-4
2
1
54) h(x) = ( x - 2)
2
-6
-8
-10
y
D)
6
4
10
2
6
4
-10 -8 -6 -4 -2-2
2
-4
-6
6 8 10 12 x
2 4
-4
-6
10
8
y
y
8
2
6 8 10 x
4
2
-4
-6
-10 -8 -6 -4 -2
-2
-8
-10
-4
-6
A)
10
-8
-10
y
8
SHORT ANSWER. Write the word or phrase that best
completes each statement or answers the question.
6
4
2
-10 -8 -6 -4 -2
-2
2
4 6
Find the distance between the pair of points.
55) (3, 4) and (7, 6)
8 10 x
-4
-6
56) (0, 10) and (9, 10)
-8
-10
Find the midpoint of the line segment whose end points
are given.
57) (-3, 1) and (-2, 2)
58) (2, 5) and (7, 4)
7
Write the standard form of the equation of the circle with
the given center and radius.
59) (8, -3); 9
Graph the equation.
63) (x - 6)2 + (y - 3)2 = 9
10
y
60) (0, -7); 9
5
61) (0, 0); 14
-10
MULTIPLE CHOICE. Choose the one alternative that
best completes the statement or answers the question.
5
-10
A)
y
10
y
5
5
-10
10 x
-5
Graph the equation and state its domain and range. Use
interval notation
62) x2 + y2 = 49
10
-5
-5
5
10 x
-10
-5
5
-5
-5
-10
-10
10 x
Domain = (3, 9), Range = (0, 6)
A)
10
B)
y
10
y
5
5
-10
-5
5
10 x
-10
-5
5
10 x
-5
-5
-10
-10
Domain = (- 7, 7); Range = (- 7, 7)
Domain = (-9, -3), Range = (-6, 0)
B)
10
y
SHORT ANSWER. Write the word or phrase that best
completes each statement or answers the question.
5
-10
-5
5
Complete the square and write the equation in standard
form. Then give the center and radius of the circle.
64) x2 + y2 - 4x - 10y + 29 = 36
10 x
-5
65) 10x2 + 10y2 = 100
-10
Domain = (-7, 7); Range = (-7, 7)
8
Find the coordinates of the vertex for the parabola defined
by the given quadratic function.
69) f(x) = (x - 2)2 - 2
MULTIPLE CHOICE. Choose the one alternative that
best completes the statement or answers the question.
Graph the equation.
66) x2 + y2 - 10x - 2y + 17 = 0
10
70) f(x) = (x - 4)2 - 4
y
Determine whether the given quadratic function has a
minimum value or maximum value. Then find the
coordinates of the minimum or maximum point.
71) f(x) = x2 + 2x - 7
5
-10
-5
5
10 x
72) f(x) = 2x2 + 2x
-5
Find the axis of symmetry of the parabola defined by the
given quadratic function.
73) f(x) = (x + 4)2 + 5
-10
A)
10
y
74) f(x) = 11(x - 3)2 + 7
5
-10
-5
5
Find the range of the quadratic function.
75) f(x) = (x + 8)2 - 7
10 x
-5
Find the y-intercept for the graph of the quadratic
function.
76) f(x) = x2 + 3x - 2
-10
B)
10
y
Find the domain and range of the quadratic function
whose graph is described.
77) The maximum is -8 at x = 1
5
-10
-5
5
10 x
Determine whether the given quadratic function has a
minimum value or maximum value. Then find the
coordinates of the minimum or maximum point.
78) f(x) = 2x2 + 2x + 1
-5
-10
79) f(x) = -5x2 - 10x
SHORT ANSWER. Write the word or phrase that best
completes each statement or answers the question.
Solve the problem.
80) You have 332 feet of fencing to enclose a
rectangular region. What is the maximum
area?
Solve the quadratic equation using the quadratic formula.
Express the solution in standard form.
67) x2 + x + 2 = 0
Find the distance between the pair of points.
81) (5, -1) and (7, -7)
68) x2 - 10x + 61 = 0
9
Complete the square and write the equation in standard
form. Then give the center and radius of the circle.
82) x2 + y 2 - 4x + 16y + 68 = 9
83) x2 + 6x + 9 + y 2 + 16y + 64 = 64
Write the standard form of the equation of the circle with
the given center and radius.
84) (-3, -6); 5
Find the midpoint of the line segment whose end points
are given.
6
6
8 2
85) ( , - ) and ( , )
5
5
5 5
Solve the problem.
86) The profit that the vendor makes per day by
selling x pretzels is given by the function
P(x) = -0.002x2 + 1.6x - 400. Find the number
of pretzels that must be sold to maximize
profit.
10
Answer Key
Testname: 112 PRACTICE TEST 1
1)
2)
3)
4)
5)
Not a function
Function
Function
y is a function of x
y is a function of x
6) 4x2 - 6x + 8
7) 5x + 9
27)
y
10
(2, 7)
5 (2, 3)
8) 1
9) function
10) not a function
11) 3.6
12) 5
13) domain: (-∞, ∞)
range: (-∞, 3]
14) domain: [0, ∞)
range: [-1, ∞)
15) domain: (-∞, ∞)
range: [0, 7]
16) (-∞, -1) or (3, ∞)
17) (-2, -1) or (3, ∞)
18) (3, ∞)
19) f has a relative maximum at x = 0; the relative
maximum is 3
20) minimum: (2, -14); maximum: (-2, 18)
21) Odd
22) Even
23) Neither
24) Odd
25) Even
26)
-10
-5
5
(-8, -3)
-5 (2, -4)
28) [0, 5)
29) 5(2x+h)
30) (-∞, ∞)
31) (-∞, ∞)
32) (4, ∞)
33) (-∞, 9) ∪ (9, ∞)
34) 5x - 5
35) -8x + 15
36) 63x2 - 37x + 4
37) (-∞, -4) or (-4, ∞)
38) Domain: -∞, 3 - 2 3 ∪ 3 - 2 3, 3 + 2 3 ∪
3 + 2 3, ∞
39) 12,375
40) 6x + 4
41) 8x2 + 4x + 6
42) (-∞, ∞)
43) (-∞, -1) or (-1, 0) or (0, ∞)
44) f(x) = |x|, g(x) = 2x + 7
45) f(x) = x8 , g(x) = 6x - 14
5
46) g(x) and h(x)
8
5
47) f-1 (x) = + 7x 7
5
x
-10
y
-5
10
48) f-1 (x) = x2 - 8
x - 5
49) f-1 (x) = 4
x
50) No
51) Yes
52) A
53) D
54) C
55) 2 5
56) 9
5 3
57) (- , )
2 2
-5
11
Answer Key
Testname: 112 PRACTICE TEST 1
9 9
58) ( , )
2 2
59) (x - 8)2 + (y + 3)2 = 81
60) x2 + (y + 7)2 = 81
61) x2 + y2 = 196
62) B
63) A
64) (x - 2)2 + (y - 5)2 = 36
(2, 5), r = 6
65) x2 + y2 = 10
(0, 0), r = 10
66) A
1
7
67) - ± i
2
2
68) {5 ± 6i}
69) (2, -2)
70) (4, -4)
71) minimum; - 1, - 8
1
1
72) minimum; - , - 2
2
73) x = -4
74) x = 3
75) [-7, ∞)
76) (0, -2)
77) Domain: (-∞, ∞)
Range: (-∞, -8]
1 1
78) minimum; - , 2 2
79) maximum; - 1, 5
80) 6889 square feet
81) 2 10
82) (x - 2)2 + (x + 8)2 = 9
(2, -8), r = 3
83) (x + 3)2 + (x + 8)2 = 64
(-3, -8), r = 8
84) (x + 3)2 + (y + 6)2 = 5
2
7
85) ( , - )
5
5
86) 400 pretzels
12