Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use point–by–point plotting to sketch the graph of the equation.
1)
y = x – 5
A)
B)
C)
D)
Answer:
D
1
2)
y =x2– 3
A)
B)
C)
D)
Answer:
C
2
Determine whether the graph is the graph of a function.
3)
A)
B)
Answer:
B
4)
A)
B)
Answer:
A
5)
A)
B)
Answer:
B
3
Determine whether the relation represents a function. If it is a function, state the domain and range.
6)
4
20
9
45
14
70
19
95
A)
function
domain:{20, 45, 70, 95}
range: {4, 9, 14, 19}
B)
function
domain: {4, 9, 14, 19}
range: {20, 45, 70, 95}
C)
not a function
Answer:
B
7)
Bob
Ann
Dave
carrots
peas
squash
A)
function
domain: {carrots, peas, squash}
range: {Bob, Ann, Dave}
B)
function
domain: {Bob, Ann, Dave}
range: {carrots, peas, squash}
C)
not a function
Answer:
C
8)
{(41, –3), (5, –2), (5, 0), (9, 2), (21, 4)}
A)
function
domain: {–3, –2, 0, 2, 4}
range: {41, 9, 5, 21}
B)
function
domain: {41, 9, 5, 21}
range: {–3, –2, 0, 2, 4}
C)
not a function
Answer:
C
9)
{(–3, 10), (–2, 5), (0, 1), (2, 5), (4, 17)}
A)
function
domain: {–3, –2, 0, 2, 4}
range: {10, 5, 1, 17}
B)
function
domain: {10, 5, 1, 17}
range: {–3, –2, 0, 2, 4}
C)
not a function
Answer:
A
Determine whether the function is linear, constant, or neither
10)
y =x + 3
7
A)
Linear
B)
Constant
C)
Neither
Answer:
A
11)
y =x3–x2+ 8
A)
Linear
B)
Constant
C)
Neither
Answer:
C
4
12)
y =2
3
A)
Linear
B)
Constant
C)
Neither
Answer:
B
13)
y – 12 = 0
A)
Linear
B)
Constant
C)
Neither
Answer:
B
Use point–by–point plotting to sketch the graph of the equation.
14)
f(x) =2x
x – 4
A)
B)
C)
D)
Answer:
C
5
The graph of a function f is given. Use the graph to answer the question.
15)
Use the graph of f given below to find f(–5).
5
–5 5
–5
A)
0
B)
8
C)
–5
D)
3
Answer:
D
Find the function value.
16)
Find f(–9) when f(x) =5–7x2.
A)
68
B)
572
C)
131
D)
–562
Answer:
D
17)
f(x) =x2– 8
x3+ 7x; f(–2)
A)
4
B)
2
11
C)
1
2
D)
–2
11
Answer:
B
18)
Given that f(x) = 5x2– 2x, find f(t + 2).
A)
t2+ 2t – 6
B)
5t2+ 18t + 16
C)
5t2– 18t + 16
D)
3t + 6
Answer:
B
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
19)
If g(x) = – 4x2+ x – 9, find g(–2), g(1), and g 3
2.
Answer:
–27, –12, –33
2
20)
For f(t) = 3t + 2 and g(t) = 2 –t2, find 4f(3) – g(–3) + g(0).
Answer:
53
6
21)
For f(t) = 3 – 5t, find f(a + h) – f(a)
h.
Answer:
–5
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Compute and simplify the difference quotient f(x +
h) – f(x)
h, h 0.
22)
f(x) = 5x2+ 7x
A)
10x + 5h + 7
B)
15x – 7h + 14
C)
10x + 7
D)
10x2+ 5h+ 7x
Answer:
A
Determine the domain of the function.
23)
f(x) = – 7x + 9
A)
B)
C)
D)
Answer:
B
24)
f(x) =x
x – 2
A)
B)
C)
D)
Answer:
C
25)
f(x) =3 – x
A)
B)
C)
D)
Answer:
B
26)
f(x) =8
x3
A)
B)
C)
D)
Answer:
D
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
27)
Only one of the following functions has domain which is not equal to all real numbers. State which function and s
domain.
(A) h(x) =4x2– 3x – 5 (B) f(x) =2x
48 – x (C) g(x) =x + 7
2
Answer:
f(x) =2x
48 – x has domain all real numbers except x = 48.
7
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x
to which there corresponds more than one value of y.
28)
x –y2= 9
A)
B)
Answer:
B
29)
y = x2– 9
A)
A function with domain
B)
Not a function; for example, when x = – 9, then y = ±1
Answer:
A
30)
xy = – 7
A)
A function with domain all real numbers except x = 0
B)
Not a function; for example, when x = – 7, y = ±1
Answer:
A
31)
xy + 3y =5
A)
A function with domain all real numbers except x = – 3
B)
Not a function; for example, when x =5, y = ±3
Answer:
A
32)
x2+ y2=49
A)
B)
Answer:
B
33)
x2–y2= 9
A)
A function with domain all real numbers except x = 5
B)
Not a function; for example, when x = 5, y = ±4
Answer:
B
Solve the problem.
34)
The function F described by F(x) = 2.75x + 71.48 can be used to estimate the height, in centimeters, of a woman
whose humerus (the bone from the elbow to the shoulder) is x cm long. Estimate the height of a woman whose
humerus is 30.93 cm long. Round your answer to the nearest four decimal places.
A)
156.5375 cm
B)
43.3000 cm
C)
105.1600 cm
D)
13.5775 cm
Answer:
A
35)
The function M described by M(x) = 2.89x + 70.64 can be used to estimate the height, in centimeters, of a male
whose humerus (the bone from the elbow to the shoulder) is x cm long. Estimate the height of a male whose
humerus is 30.93 cm long. Round your answer to the nearest four decimal places.
A)
157.3400 m
B)
30.9300 cm
C)
160.0277 cm
D)
156.5375 cm
Answer:
C
36)
To estimate the ideal minimum weight of a woman in pounds multiply her height in inches by 4 and subtract
130. Let W = the ideal minimum weight and h = height. W is a linear function of h. Find the ideal minimum
weight of a woman whose height is 62 inches.
A)
378 lb
B)
130 lb
C)
118 lb
D)
120 lb
Answer:
C
8
37)
The point at which a company’s costs equals its revenue is the break–even. C represents cost, in dollars, of x units
of a product. R represents the revenue, in dollars, for the sale of x units. Find the number of units that must be produced
and sold in order to break even.
C = 15x + 12,000
R = 18x – 6000
A)
800
B)
12,000
C)
545
D)
6000
Answer:
D
38)
The function P, given by P(d) =1
33 d + 1, gives the pressure, in atmospheres (atm), at a depth d, in feet, under
the sea. Find the pressure at 200 feet. Round your answer to the nearest whole number.
A)
201 atm
B)
8 atm
C)
7 atm
D)
200 atm
Answer:
C
39)
To estimate the ideal minimum weight of a woman in pounds multiply her height in inches by 4 and subtract
130. Let W = the ideal minimum weight and h = height. Express W as a linear function of h.
A)
W(h) = 4 (h + 130)
B)
W(h) = 4h – 130
C)
W(h) = 130
D)
W(h) = 130h + 4
Answer:
B
Provide an appropriate response.
40)
In a profit–loss analysis, point where revenue equals cost.
A)
profit–loss point
B)
inflection point
C)
turning point
D)
break–even point
Answer:
D
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
41)
Let T be the set of teachers at a high school and let S be the set of students enrolled at that school. Determine which of
the following correspondences define a function. Explain.
(A) A student corresponds to the teacher if the student is enrolled in the teacher’s class.
(B) A student corresponds to every teacher of the school.
Answer:
Choice (A) defines a function. To each element (student) of the first set (or domain), there corresponds exactly
one element (teacher) of the second set (or range).
Choice (B) does not define a function. An element (student) of the first set (or domain) corresponds to more tha
one element (teacher) of the second set (or range).
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Give the domain and range of the function.
42)
f(x) =x2+2
A)
B)
C)
D)
Answer:
B
43)
g(x) =x2–4
A)
B)
C)
D)
Answer:
C
9
44)
h(x) = – 4 x
A)
B)
C)
D)
Answer:
D
45)
s(x) =1– x
A)
B)
C)
D)
Answer:
C
46)
r(x) =x –7–9
A)
Domain: all real numbers; Range: [0, )
B)
Domain: all real numbers; Range: all real numbers
C)
Domain: [– 9, ); Range: all real numbers
D)
Domain: all real numbers; Range: [– 9, )
Answer:
D
Provide an appropriate response.
47)
How can the graph of f(x) = – x + 1 be obtained from the graph of y =x?
A)
Shift it horizontally –1 units to the left. Reflect it across the x–axis.
B)
Shift it horizontally 1 units to the right. Reflect it across the x–axis.
C)
Shift it horizontally 1 units to the left. Reflect it across the y–axis.
D)
Shift it horizontally 1 units to the left. Reflect it across the x–axis.
Answer:
D
48)
How can the graph of f(x) = – (x –1 )2 6 be obtained from the graph of y =x2?
A)
Shift it horizontally 1 units to the left. Reflect it across the x–axis. Shift it 6 units up.
B)
Shift it horizontally 1 units to the right. Reflect it across the y–axis. Shift it 6 units down.
C)
Shift it horizontally 1 units to the right. Reflect it across the y–axis. Shift it 6 units up.
D)
Shift it horizontally 1 units to the right. Reflect it across the x–axis. Shift it 6 units up.
Answer:
D
Write an equation for a function that has a graph with the given transformations.
49)
The shape of y =x is shifted 5 units to the left. Then the graph is shifted 7 units upward.
A)
f(x) =x – 5 + 7
B)
f(x) =x + 7 + 5
C)
f(x) = 7 x + 5
D)
f(x) =x + 5 + 7
Answer:
D
50)
The shape of y =x2 is vertically stretched by a factor of 10, and the resulting graph is reflected across the x–axis.
A)
f(x) = – 10x2
B)
f(x) = 10x2
C)
f(x) = 10(x – 10)2
D)
f(x) =(x – 10)2
Answer:
A
10
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
51)
The following graph represents the result of applying a sequence of transformations to the graph of a basic
function. Identify the basic function and describe the transformation(s). Write the equation for the given graph.
Answer:
Basic function is f(x) =x2; shift right 2 units, shift up 5 units. f(x) =(x – 2)2+ 5
52)
The following graph represents the result of applying a sequence of transformations to the graph of a basic
function. Identify the basic function and describe the transformation(s). Write the equation for the given graph.
Answer:
Basic function is f(x) =x; reflect over the x –axis, shift left 4 units, shift down 2 units. f(x) = – x + 4 –2
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Graph the function.
11
53)
f(x) =x + 2 if x < 1
1if x 1
A)
B)
C)
D)
Answer:
A
12
54)
f(x) =–x + 3 if x < 2
2x – 3 if x 2
A)
B)
C)
D)
Answer:
C
13
55)
Assume it costs 25 cents to mail a letter weighing one ounce or less, and then 20 cents for each additional ounce
or fraction of an ounce. Let L(x) be the cost of mailing a letter weighing x ounces. Graph y = L(x). Use the
interval (0, 4].
A)
B)
C)
D)
Answer:
B
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
56)
If f(x) =x – 3 if x < 2
x2 if x 2 , what is the definition of g(x), the function whose graph is obtained by shifting f(x)’s
graph right 5 units and down 1 unit?
Answer:
g(x) =x – 9 x < 7
(x – 5)2– 1 x 7
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
14
57)
A retail chain sells washing machines. The retail price p(x) (in dollars) and the weekly demand x for a particular
model are related by the function p(x) = 625 – 5 x, where 50 x 500. (i) Describe how the graph of the
function p can be obtained from the graph of one of the six basic functions: y = x, y =x2,y =x3, y =x, y =3x,
or y =x. (ii) Sketch a graph of function p using part (i) as an aid.
A)
B)
C)
D)
Answer:
A
15
58)
The following table shows a recent state income tax schedule for married couples filing a joint return in State X.
State X Income Tax
SCHEDULE I – MARRIED FILING JOINTLY
If taxable income is
Over But not over Tax due is
$0 $40,000 4.25% of taxable incomes
$40,000 $70,000 $3700 plus 6.75% of excess over $40,000
$70,000 $3875 plus 7.05% of excess over $70,000
(i) Write a piecewise definition for the tax due T(x) on an income of x dollars. (ii) Graph T(x). (iii) Find the tax due on a
taxable income of $50,000. Of $95,000.
A)
B)
16
C)
D)
Answer:
D
59)
The average weight of a particular species of frog is given by w(x) = 98x3, 0.1 x 0.3, where x is length (with
legs stretched out) in meters and w(x) is weight in grams. (i) Describe how the graph of function w can be
obtained from one of the six basic functions: y = x, y =x2, y =x3, y =x, y =3x, or y =x. (ii) Sketch a graph of
function w using part (i) as an aid.
17
A)
B)
C)
D)
Answer:
B
Find the x–intercept(s) if they exist.
60)
x2+ 6x + 5 = 0
A)
–1, –5
B)
1 , 5
C)
10, –5
D)
5, –5
Answer:
A
61)
6x2= 42x
A)
0
B)
0, 7
C)
7
D)
21
Answer:
B
18
For the given function, find each of the following:
(A) Intercepts
(B) Vertex
(C) Maximum or minimum
(D) Range
62)
f(x) =(x + 2)2– 9
A)
B)
C)
D)
Answer:
B
63)
g(x) =(x – 3)2– 1
A)
B)
C)
D)
Answer:
A
64)
m(x) = – (x + 1)2+ 4
A)
B)
C)
D)
Answer:
B
65)
n(x) = – (x – 1)2+ 4
A)
B)
C)
D)
Answer:
A
Find the vertex form for the quadratic function. Then find each of the following:
(A) Intercepts
(B) Vertex
(C) Maximum or minimum
(D) Range
66)
f(x) =x2+ 2x – 8
A)
B)
C)
D)
Answer:
C
67)
g(x) =x2– 2x – 3
A)
B)
C)
D)
Answer:
B
20