Practice test #1 This inaddition to the homework, quizzes , textbook and notes need to be studied in order to be prepared for this test.
SHORT ANSWER. Write the word or phrase that best
completes each statement or answers the question.
Use the vertical line test to determine whether or not the
graph is a graph in which y is a function of x.
11)
Give the domain and range of the relation.
1) {(-7, -6), (-3, 2), (-5, 5), (-5, 8)}
y
2) {(5, -7), (-2, -5), (-6, -4), (-3, 6), (1, -6)}
Determine whether the relation is a function.
3) {(-4, -7), (-1, -8), (1, -5), (7, 3)}
x
4) {(-7, -7), (-7, -8), (-1, 4), (6, 5), (10, -1)}
Determine whether the equation defines y as a function of
x.
5) x2 + y2 = 1
12)
y
6) y2 = 6x
7) x = y2
x
Evaluate the function at the given value of the
independent variable and simplify.
x2 + 7
8) f(x) =
; f(5)
x3 + 2x
9) f(x) =
x + 13;
f(-4)
Use the graph to find the indicated function value.
13) y = f(x). Find f(-5)
Solve the problem.
10) The total cost in dollars for a certain company
to produce x empty jars to be used by a jelly
producer is given by the function C(x) = 0.7x +
29,000. Find C(70,000), the cost of producing
70,000 jars.
5
y
4
3
2
1
-5
-4
-3
-2
-1
1
-1
-2
-3
-4
-5
1
2
3
4
5 x
Use the graph to determine the function's domain and
range.
14)
6
Identify the intervals where the function is changing as
requested.
17) Constant
y
5
5
4
4
3
3
2
2
1
1
-6 -5 -4 -3 -2 -1
-1
y
1
2
3
4
5
6 x
-5
-4
-3
-2
-1
1
2
3
4
5 x
12
x
4
5 x
-1
-2
-2
-3
-4
-3
-5
-4
-6
-5
18) Increasing
Identify the intercepts.
15)
y
8
y
10
4
5
-12
-10
-5
5
10
-6
6
x
-4
-5
-8
-10
19) Decreasing
16)
5
y
10
y
4
3
5
2
1
-10
-5
5
10
x
-5
-4
-3
-2
-1
1
-1
-5
-2
-3
-10
-4
-5
2
2
3
Use the graph of the given function to find any relative
maxima and relative minima.
20) f(x) = x3 - 3x2 + 1
5
24)
y
10
8
y
6
4
4
2
3
2
-10 -8 -6 -4 -2
-2
1
-4
2
4
6
8 10 x
-6
-5
-4
-3
-2
-1
1
2
3
4
5 x
-8
-1
-10
-2
-3
Evaluate the piecewise function at the given value of the
independent variable.
x2 - 3
if x ≠ 7
25) h(x) = x - 7
; h(7)
-4
-5
x-8
Determine whether the given function is even, odd, or
neither.
21) f(x) = x5 - x4
Graph the function.
26) f(x) = x + 4
-2
22) f(x) = x3 - 3x
if x = 7
if x < 1
if x ≥ 1
y
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.
23)
-5
y
5
x
10
8
6
-5
4
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10 x
x+5
27) f(x) = -4
-x + 5
-4
-6
-8
if -8 ≤ x < 2
if x = 2
if x > 2
y
-10
10
5
-10
-5
5
-5
-10
3
10
x
Find and simplify the difference quotient
f(x + h) - f(x)
, h≠ 0 for the given function.
h
Use the graph of the function f, plotted with a solid line, to
sketch the graph of the given function g.
31) g(x) = -f(x - 2) - 2
28) f(x) = 6x + 7
6
5
4
3
2
1
Begin by graphing the standard square root function f(x) =
x . Then use transformations of this graph to graph the
given function.
29) h(x) = -x + 1 + 2
10
8
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
y
6
y
y = f(x)
1 2 3 4 5 6 x
4
2
-10 -8 -6 -4 -2-2
2
4
Find the domain of the function.
32) f(x) = x2 + 5
6 8 10 x
-4
-6
-8
Find and simplify the difference quotient
f(x + h) - f(x)
, h≠ 0 for the given function.
h
-10
Begin by graphing the standard cubic function f(x) = x 3 .
Then use transformations of this graph to graph the given
function.
30) h(x) = (x + 3)3 - 2
10
33) f(x) = x2 + 9x - 7
Find the domain of the function.
34) f(x) = 6 - x
y
35)
8
6
4
2
-10 -8 -6 -4 -2-2
x
x-4
36) f(x) =
2
4
6 8 10 x
1
4
+
x-2 x+6
-4
Given functions f and g, perform the indicated operations.
37) f(x) = 9 - 6x,
g(x) = -2x + 6
Find f + g.
-6
-8
-10
Given functions f and g, determine the domain of f + g.
2
38) f(x) = 5x + 10,
g(x) =
x-9
Find the domain of the indicated combined function.
39) Find the domain of (fg)(x) when f(x) = 6x + 5
and g(x) = 5x - 4.
4
For the given functions f and g , find the indicated
composition.
40) f(x) = 20x2 - 5x, g(x) = 14x - 3
Does the graph represent a function that has an inverse
function?
52)
y
(f∘g)(2)
41) f(x) = 4x2 + 2x + 5,
(g∘f)(x)
42) f(x) =
x-4
,
5
g(x) = 2x - 4
x
g(x) = 5x + 4
(g∘f)(x)
Find the domain of the composite function f∘g.
6
43) f(x) =
,
g(x) = x + 2
x+7
44) f(x) =
x;
Use the graph of f to draw the graph of its inverse
function.
53)
g(x) = 5x + 25
y
Find functions f and g so that h(x) = (f ∘ g)(x).
45) h(x) = (6x - 14)8
10
5
42x2 + 5
46) h(x) =
-10
-5
Determine which two functions are inverses of each other.
x-6
x+6
47) f(x) =
g(x) = 4x - 6
h(x) =
4
4
48) f(x) = x3 - 4
g(x) =
3
x-4
x
5
10
x
-10
h(x) = x3 + 4
54)
y
10
5
x+8
-10
51) f(x) =
10
-5
Find the inverse of the one-to-one function.
5
49) f(x) =
7x - 8
50) f(x) =
5
3
-5
-5
x-6
-10
5
The graph of a quadratic function is given. Determine the
function's equation.
57)
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 .
y
55) f(x) = x2 - 6, x ≥ 0
10
8
10
6
y
4
8
2
6
-10 -8 -6 -4 -2-2
4
-6
-4
4 6
8 10
x
2
4 6
8 10
x
-4
-6
2
-10 -8
2
-2
2
4
6
8
-8
x
-10
-2
-4
-6
58)
-8
y
-10
10
8
6
56) f(x) = (x - 4)2 , x ≥ 4
4
2
10
y
-10 -8 -6 -4 -2-2
8
-4
-6
6
-8
4
-10
2
-10 -8
-6
-4
-2
2
4
6
8
x
Find the coordinates of the vertex for the parabola defined
by the given quadratic function.
59) f(x) = 7 - (x + 4)2
-2
-4
-6
-8
60) f(x) = x2 + 14x + 3
-10
Find the x-intercepts (if any) for the graph of the quadratic
function.
61) f(x) = (x - 1)2 - 1
62) f(x) = x2 + 18x + 70 Give your answers in
exact form.
6
Use the vertex and intercepts to sketch the graph of the
quadratic function.
63) f(x) = x2 + 6x + 5
68) The cost in millions of dollars for a company to
manufacture x thousand automobiles is given
by the function C(x) = 5x2 - 40x + 144. Find the
number of automobiles that must be produced
to minimize the cost.
y
10
5
-10
-5
5
10
x
5
10
x
-5
-10
64) f(x) = 1 - (x - 1)2
y
10
5
-10
-5
-5
-10
Determine whether the given quadratic function has a
minimum value or maximum value. Then find the
coordinates of the minimum or maximum point.
65) f(x) = 2x2 + 2x + 1
66) f(x) = 3x2 + 9x
Solve the problem.
67) A rain gutter is made from sheets of aluminum
that are 18 inches wide by turning up the
edges to form right angles. Determine the
depth of the gutter that will maximize its
cross-sectional area and allow the greatest
amount of water to flow.
7
Answer Key
Testname: PRACTICE TEST 112 1
1)
2)
3)
4)
5)
6)
7)
domain = {-5, -3, -7}; range = {5, 2, -6, 8}
domain = {5, 1, -6, -3, -2}; range = {-7, -6, -4, 6, -5}
Function
Not a function
y is not a function of x
y is not a function of x
y is not a function of x
32
8)
135
9) 3
10) $78,000
11) function
12) function
13) 5
14) domain: (-∞, ∞)
range: (-∞, 3]
15) (8, 0), (-8, 0), (0, 6), (0, -6)
16) (7, 0), (-7, 0), (0, -7)
17) (-∞, -1) or (3, ∞)
18) (0, 5)
19) (-3, -2)
20) maximum: (0, 1); minimum: (2, -3)
21) Neither
22) Odd
23) Neither
24) Even
25) -1
26)
y
5
(1, 5)
-5
5
x
(1, -2)
-5
8
Answer Key
Testname: PRACTICE TEST 112 1
27)
y
10
(2, 7)
5
-10
(2, 3)
-5
5
(-8, -3)
10
x
-5 (2, -4)
-10
28) 6
29)
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
30)
10
y
8
6
4
2
-10 -8 -6 -4 -2-2
-4
-6
-8
-10
31)
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
9
Answer Key
Testname: PRACTICE TEST 112 1
32) (-∞, ∞)
33) 2x + h + 9
34) (-∞, 6]
35) (4, ∞)
36) (-∞, -6) ∪ (-6, 2) ∪ (2, ∞)
37) -8x + 15
38) (-∞, 9) or (9, ∞)
4
39) Domain: , ∞
5
40) 12,375
41) 8x2 + 4x + 6
42) x
43) (-∞, -9) or (-9, ∞)
44) [-5, ∞)
45) f(x) = x8 , g(x) = 6x - 14
46) f(x) = x, g(x) = 42x2 + 5
47) g(x) and h(x)
48) g(x) and h(x)
5
8
49) f-1 (x) =
+
7x 7
50) f-1 (x) = x2 - 8
51) f-1 (x) = x3 + 6
52) No
53)
y
10
5
-10
-5
5
10
x
-5
-10
10
Answer Key
Testname: PRACTICE TEST 112 1
54)
y
10
5
-10
-5
5
x
10
-5
-10
55)
10
y
8
6
4
2
-10 -8
-6
-4
-2
2
4
6
8
x
-2
-4
-6
-8
-10
f domain = (0, ∞); range = (-6, ∞)
f -1 domain = (0, ∞); range = (-6, ∞)
56)
10
y
8
6
4
2
-10 -8
-6
-4
-2
2
4
6
8
x
-2
-4
-6
-8
-10
f domain = (4, ∞); range = (0, ∞)
f -1 domain = (0, ∞); range = (4, ∞)
57) g(x) = (x + 1)2 - 1
58) j(x) = (x - 3)2 - 3
11
Answer Key
Testname: PRACTICE TEST 112 1
59) (-4, 7)
60) (-7, -46)
61) (0, 0) and (2, 0)
62) (-9 ± 11, 0)
63)
y
10
5
-10
-5
5
10
x
5
10
x
-5
-10
64)
y
10
5
-10
-5
-5
-10
65) minimum; -
1 1
,
2 2
66) minimum; -
3
27
,2
4
67) 4.5 inches
68) 4 thousand automobiles
12