Determine whether each relation is a function.
Explain.
1.
ANSWER:
Yes; for each input there is exactly one output.
2.
ANSWER:
No; the domain value 6 is paired with both 9 and 10.
3.{(2, 2), (−1, 5), (5, 2), (2, −4)}
ANSWER:
No; the domain value 2 is paired with 2 and −4.
4.
ANSWER:
Yes; the graph passes the vertical line test.
5.
ANSWER:
No; when x = 0, y = 1 and y = 6.
6.
ANSWER:
Yes; the graph passes the vertical line test.
7.
ANSWER:
Yes; the graph passes the vertical line test.
8.
ANSWER:
No; the graph does not pass the vertical line test.
9.SCHOOL ENROLLMENT The table shows the
total enrollment in U.S. public schools.
a. Write a set of ordered pairs representing the data
in the table if x is the number of school years since
2004-2005.
b. Draw a graph showing the relationship between
the year and enrollment.
c. Describe the domain and range of the data.
ANSWER:
a. {(0, 48,560), (1, 48,710), (2, 48,948), (3, 49,091)}
b.
c. The domain is the school year and the range is the
enrollment.
10.CCSS REASONING The cost of sending cell
phone pictures is given by y = 0.25x, where x is the
number of pictures sent, and y isthecostindollars.
a. Write the equation in function notation. Interpret
thefunctionintermsofthecontext.
b. Find f(5) and f(12). What do these values
represent?
c. Determine the domain and range of this function.
ANSWER:
a.f(x) = 0.25x
b. f(5) = $1.25, f(12) = $3.00; These values
represent the cost to send five and twelve pictures,
respectively.
c. The domain is the number of pictures sent and the
cost is the range.
If f(x) = 6x + 7 and g(x) = x2 − 4, find each
value.
11.f(−3)
ANSWER:
−11
12.f(m)
ANSWER:
6m + 7
13.f(r − 2)
ANSWER:
6r − 5
14.g(5)
ANSWER:
21
15.g(a) + 9
ANSWER:
a2 + 5
16.g(−4t)
ANSWER:
16t2 −4
17.f(q + 1)
ANSWER:
6q + 13
18.f(2) + g(2)
ANSWER:
19
19.g(−b)
ANSWER:
b2 − 4
Determine whether each relation is a function.
Explain.
20.
ANSWER:
yes; for each input there is exactly one output.
21.
ANSWER:
no; the domain value 4 is paired with both 5 and 6.
22.
ANSWER:
no; the domain value −5 is paired with both 3 and 5.
23.
ANSWER:
yes; for each input there is exactly one output.
24.
ANSWER:
no; when x = 4, y = 4 and y = 6.
25.
ANSWER:
yes; the graph passes the vertical line test.
26.CCSS SENSE-MAKING The table shows the
median home prices in the United States, from 2007
to 2009.
a. Write a set of ordered pairs representing the data
in the table.
b. Draw a graph showing the relationship between
the year and price.
c. What is the domain and range for this data?
ANSWER:
a. {(2007, 234,300), (2008, 213,200), (2009, 212,200)}
b.
c. The domain is the year. The range is the median
home price.
Determine whether each relation is a function.
27.{(5, −7), (6, −7), (−8, −1), (0, −1)}
ANSWER:
yes
28.{(4, 5), (3, −2), (−2, 5), (4, 7)}
ANSWER:
no
29.y = −8
ANSWER:
yes
30.x = 15
ANSWER:
no
31.y = 3x −2
ANSWER:
yes
32.y = 3x + 2y
ANSWER:
yes
If f(x) = −2x − 3 and g(x) = x2 + 5x, find each
value.
33.
f(−1)
ANSWER:
−1
34.
f(6)
ANSWER:
−15
35.g(2)
ANSWER:
14
36.g(−3)
ANSWER:
−6
37.g(−2) + 2
ANSWER:
−4
38.
f(0) − 7
ANSWER:
−10
39.
f(4y)
ANSWER:
−8y − 3
40.g(−6m)
ANSWER:
36m2 − 30m
41.
f(c − 5)
ANSWER:
−2c + 7
42.
f(r + 2)
ANSWER:
−2r − 7
43.5[f(d)]
ANSWER:
−10d − 15
44.3[g(n)]
ANSWER:
3n2 + 15n
45.EDUCATION The average national math test
scores f(t) for 17-year-olds can be represented as a
function of the national science scores t by f(t) = 0.8t
+ 72.
a. Graph this function. Interpret the function in terms
of the context.
b. What is the science score that corresponds to a
math score of 308?
c. What is the domain and range of this function?
ANSWER:
a.
When the science score is 0, the math score is 72.
Foreachpointthesciencescoreincreases,
the math score increases by 0.8 point.
b. 295
c. The domain is the set of science scores. The
range is the set of math scores.
Determine whether each relation is a function.
46.
ANSWER:
yes
47.
ANSWER:
yes
48.BABYSITTING Christina earns $7.50 an hour
babysitting.
a. Write an algebraic expression to represent the
money Christina will earn if she works h hours.
b. Choose five values for the number of hours
Christina can babysit. Create a table with h and the
value for the amount of money she will make during
that time.
c. Use the values in your table to create a graph.
d. Does it make sense to connect the points in your
graph with a line? Why or why not?
ANSWER:
a. $7.50h
b. Sample answer:
c.
d. Yes, because they could pay Christina for partial
hours that she worked.
49.OPEN ENDED Write a set of three ordered pairs
that represent a function. Choose another display that
represents this function.
ANSWER:
Sample answer: {(–2, 3), (0, 3), (2, 5)};
50.REASONING The set of ordered pairs {(0, 1), (3,
2), (3, −5), (5, 4)} represents a relation between x
and y. Graph the set of ordered pairs. Determine
whether the relation is a function. Explain.
ANSWER:
Not a function; one member of the domain, 3, is
paired with two different members of the range, −5
and 2.
51.CHALLENGE Consider f(x) = −4.3x − 2. Write f(g
+ 3.5) and simplify by combining like terms.
ANSWER:
f(g + 3.5) = −4.3g − 17.05
52.WRITE A QUESTION A classmate graphed a set
of ordered pairs and used the vertical line test to
determine whether it was a function. Write a
question to help her decide if the same strategy can
be applied to a mapping.
ANSWER:
Sample answer: Isn’t a mapping another
representation of a set of ordered pairs?
53.CCSS PERSEVERENCE If f(3b − 1) = 9b − 1,
find one possible expression for f(x).
ANSWER:
Sample answer: f(x) = 3x + 2
54.ERROR ANALYSIS Corazon thinks f(x) and g(x)
are representations of the same function. Maggie
disagrees. Who is correct? Explain your reasoning.
ANSWER:
Maggie; the graph represents f (x ) = –2x + 1 and
the table represents g(x ) = –2x – 1.
55.WRITING IN MATH How can you determine
whether a relation represents a function?
ANSWER:
Sample answer: You can determine whether each
element of the domain is paired with exactly one
element of the range. For example, if given a graph,
you could use the vertical line test; if a vertical line
intersects the graph more than once, then the relation
that the graph represents is not a function.
56.Which point on the number line represents a number
whose square is less than itself?
A A
B B
C C
D D
ANSWER:
B
57.Determine which of the following relations is a
function.
F {(−3, 2), (4, 1), (−3, 5)}
G {(2, −1), (4, −1), (2, 6)}
H {(−3, −4), (−3, 6), (8, −2)}
J {(5, −1), (3, −2), (−2, −2)}
ANSWER:
J
58.GEOMETRY What is the value of x?
A 3 in
B 4 in.
C 5 in.
D 6 in.
ANSWER:
A
59.SHORT RESPONSE Camille made 16 out of 19 of
her serves during her first volleyball game. She made
13 out of 16 of her serves during her second game.
During which game did she make a greater percent
of her serves?
ANSWER:
her first game
Solve each equation.
60.
ANSWER:
3
61.
ANSWER:
62.z = 32 + 4(−3)
ANSWER:
20
63.SCHOOL SUPPLIES The table shows the prices
of some items Tom needs. If he needs 4 glue sticks,
10 pencils, and 4 notebooks, write and evaluate an
expression to determine Tom’scost.
ANSWER:
4($1.99) + 10(0.25) + (1.85) = 17.86, so the cost is
$17.86.
Write a verbal expression for each algebraic
expression.
64.4y + 2
ANSWER:
Sample answer: four times y plus two
65.
ANSWER:
Sample answer: two thirds times x
66.a2b + 5
ANSWER:
Sample answer: a squared times b plus 5
Find the volume of each rectangular prism.
67.
ANSWER:
38.016 cm3
68.
ANSWER:
in.3
69.
ANSWER:
288,000 mm3
Evaluate each expression.
70.If x = 3, then 6x − 5 = ?.
ANSWER:
13
71.If n = −1, then 2n + 1 = ?.
ANSWER:
−1
72.If p = 4, then 3p + 4 = ?.
ANSWER:
16
73.If q = 7, then 7q − 9 = ?.
ANSWER:
40
74.If y = 10, then 8y − 15 = ? .
ANSWER:
65
75.If k = −11, then 4k + 6 = ? .
ANSWER:
−38
Determine whether each relation is a function.
Explain.
1.
ANSWER:
Yes; for each input there is exactly one output.
2.
ANSWER:
No; the domain value 6 is paired with both 9 and 10.
3.{(2, 2), (−1, 5), (5, 2), (2, −4)}
ANSWER:
No; the domain value 2 is paired with 2 and −4.
4.
ANSWER:
Yes; the graph passes the vertical line test.
5.
ANSWER:
No; when x = 0, y = 1 and y = 6.
6.
ANSWER:
Yes; the graph passes the vertical line test.
7.
ANSWER:
Yes; the graph passes the vertical line test.
8.
ANSWER:
No; the graph does not pass the vertical line test.
9.SCHOOL ENROLLMENT The table shows the
total enrollment in U.S. public schools.
a. Write a set of ordered pairs representing the data
in the table if x is the number of school years since
2004-2005.
b. Draw a graph showing the relationship between
the year and enrollment.
c. Describe the domain and range of the data.
ANSWER:
a. {(0, 48,560), (1, 48,710), (2, 48,948), (3, 49,091)}
b.
c. The domain is the school year and the range is the
enrollment.
10.CCSS REASONING The cost of sending cell
phone pictures is given by y = 0.25x, where x is the
number of pictures sent, and y isthecostindollars.
a. Write the equation in function notation. Interpret
thefunctionintermsofthecontext.
b. Find f(5) and f(12). What do these values
represent?
c. Determine the domain and range of this function.
ANSWER:
a.f(x) = 0.25x
b. f(5) = $1.25, f(12) = $3.00; These values
represent the cost to send five and twelve pictures,
respectively.
c. The domain is the number of pictures sent and the
cost is the range.
If f(x) = 6x + 7 and g(x) = x2 − 4, find each
value.
11.f(−3)
ANSWER:
−11
12.f(m)
ANSWER:
6m + 7
13.f(r − 2)
ANSWER:
6r − 5
14.g(5)
ANSWER:
21
15.g(a) + 9
ANSWER:
a2 + 5
16.g(−4t)
ANSWER:
16t2 −4
17.f(q + 1)
ANSWER:
6q + 13
18.f(2) + g(2)
ANSWER:
19
19.g(−b)
ANSWER:
b2 − 4
Determine whether each relation is a function.
Explain.
20.
ANSWER:
yes; for each input there is exactly one output.
21.
ANSWER:
no; the domain value 4 is paired with both 5 and 6.
22.
ANSWER:
no; the domain value −5 is paired with both 3 and 5.
23.
ANSWER:
yes; for each input there is exactly one output.
24.
ANSWER:
no; when x = 4, y = 4 and y = 6.
25.
ANSWER:
yes; the graph passes the vertical line test.
26.CCSS SENSE-MAKING The table shows the
median home prices in the United States, from 2007
to 2009.
a. Write a set of ordered pairs representing the data
in the table.
b. Draw a graph showing the relationship between
the year and price.
c. What is the domain and range for this data?
ANSWER:
a. {(2007, 234,300), (2008, 213,200), (2009, 212,200)}
b.
c. The domain is the year. The range is the median
home price.
Determine whether each relation is a function.
27.{(5, −7), (6, −7), (−8, −1), (0, −1)}
ANSWER:
yes
28.{(4, 5), (3, −2), (−2, 5), (4, 7)}
ANSWER:
no
29.y = −8
ANSWER:
yes
30.x = 15
ANSWER:
no
31.y = 3x −2
ANSWER:
yes
32.y = 3x + 2y
ANSWER:
yes
If f(x) = −2x − 3 and g(x) = x2 + 5x, find each
value.
33.
f(−1)
ANSWER:
−1
34.
f(6)
ANSWER:
−15
35.g(2)
ANSWER:
14
36.g(−3)
ANSWER:
−6
37.g(−2) + 2
ANSWER:
−4
38.
f(0) − 7
ANSWER:
−10
39.
f(4y)
ANSWER:
−8y − 3
40.g(−6m)
ANSWER:
36m2 − 30m
41.
f(c − 5)
ANSWER:
−2c + 7
42.
f(r + 2)
ANSWER:
−2r − 7
43.5[f(d)]
ANSWER:
−10d − 15
44.3[g(n)]
ANSWER:
3n2 + 15n
45.EDUCATION The average national math test
scores f(t) for 17-year-olds can be represented as a
function of the national science scores t by f(t) = 0.8t
+ 72.
a. Graph this function. Interpret the function in terms
of the context.
b. What is the science score that corresponds to a
math score of 308?
c. What is the domain and range of this function?
ANSWER:
a.
When the science score is 0, the math score is 72.
Foreachpointthesciencescoreincreases,
the math score increases by 0.8 point.
b. 295
c. The domain is the set of science scores. The
range is the set of math scores.
Determine whether each relation is a function.
46.
ANSWER:
yes
47.
ANSWER:
yes
48.BABYSITTING Christina earns $7.50 an hour
babysitting.
a. Write an algebraic expression to represent the
money Christina will earn if she works h hours.
b. Choose five values for the number of hours
Christina can babysit. Create a table with h and the
value for the amount of money she will make during
that time.
c. Use the values in your table to create a graph.
d. Does it make sense to connect the points in your
graph with a line? Why or why not?
ANSWER:
a. $7.50h
b. Sample answer:
c.
d. Yes, because they could pay Christina for partial
hours that she worked.
49.OPEN ENDED Write a set of three ordered pairs
that represent a function. Choose another display that
represents this function.
ANSWER:
Sample answer: {(–2, 3), (0, 3), (2, 5)};
50.REASONING The set of ordered pairs {(0, 1), (3,
2), (3, −5), (5, 4)} represents a relation between x
and y. Graph the set of ordered pairs. Determine
whether the relation is a function. Explain.
ANSWER:
Not a function; one member of the domain, 3, is
paired with two different members of the range, −5
and 2.
51.CHALLENGE Consider f(x) = −4.3x − 2. Write f(g
+ 3.5) and simplify by combining like terms.
ANSWER:
f(g + 3.5) = −4.3g − 17.05
52.WRITE A QUESTION A classmate graphed a set
of ordered pairs and used the vertical line test to
determine whether it was a function. Write a
question to help her decide if the same strategy can
be applied to a mapping.
ANSWER:
Sample answer: Isn’t a mapping another
representation of a set of ordered pairs?
53.CCSS PERSEVERENCE If f(3b − 1) = 9b − 1,
find one possible expression for f(x).
ANSWER:
Sample answer: f(x) = 3x + 2
54.ERROR ANALYSIS Corazon thinks f(x) and g(x)
are representations of the same function. Maggie
disagrees. Who is correct? Explain your reasoning.
ANSWER:
Maggie; the graph represents f (x ) = –2x + 1 and
the table represents g(x ) = –2x – 1.
55.WRITING IN MATH How can you determine
whether a relation represents a function?
ANSWER:
Sample answer: You can determine whether each
element of the domain is paired with exactly one
element of the range. For example, if given a graph,
you could use the vertical line test; if a vertical line
intersects the graph more than once, then the relation
that the graph represents is not a function.
56.Which point on the number line represents a number
whose square is less than itself?
A A
B B
C C
D D
ANSWER:
B
57.Determine which of the following relations is a
function.
F {(−3, 2), (4, 1), (−3, 5)}
G {(2, −1), (4, −1), (2, 6)}
H {(−3, −4), (−3, 6), (8, −2)}
J {(5, −1), (3, −2), (−2, −2)}
ANSWER:
J
58.GEOMETRY What is the value of x?
A 3 in
B 4 in.
C 5 in.
D 6 in.
ANSWER:
A
59.SHORT RESPONSE Camille made 16 out of 19 of
her serves during her first volleyball game. She made
13 out of 16 of her serves during her second game.
During which game did she make a greater percent
of her serves?
ANSWER:
her first game
Solve each equation.
60.
ANSWER:
3
61.
ANSWER:
62.z = 32 + 4(−3)
ANSWER:
20
63.SCHOOL SUPPLIES The table shows the prices
of some items Tom needs. If he needs 4 glue sticks,
10 pencils, and 4 notebooks, write and evaluate an
expression to determine Tom’scost.
ANSWER:
4($1.99) + 10(0.25) + (1.85) = 17.86, so the cost is
$17.86.
Write a verbal expression for each algebraic
expression.
64.4y + 2
ANSWER:
Sample answer: four times y plus two
65.
ANSWER:
Sample answer: two thirds times x
66.a2b + 5
ANSWER:
Sample answer: a squared times b plus 5
Find the volume of each rectangular prism.
67.
ANSWER:
38.016 cm3
68.
ANSWER:
in.3
69.
ANSWER:
288,000 mm3
Evaluate each expression.
70.If x = 3, then 6x − 5 = ?.
ANSWER:
13
71.If n = −1, then 2n + 1 = ?.
ANSWER:
−1
72.If p = 4, then 3p + 4 = ?.
ANSWER:
16
73.If q = 7, then 7q − 9 = ?.
ANSWER:
40
74.If y = 10, then 8y − 15 = ? .
ANSWER:
65
75.If k = −11, then 4k + 6 = ? .
ANSWER:
−38
eSolutionsManual-PoweredbyCogneroPage1
1-7 Functions
