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© 2023 Jean Adams Flamingo Math.com Unit 2
2.4 – 2.7 Quiz
Form A
1.
The function 𝑓𝑓
is given by 𝑓𝑓
𝑥𝑥
=
𝑥𝑥
2
−
4
and the function 𝑔𝑔
is given by 𝑔𝑔
𝑥𝑥
=
𝑥𝑥+3
𝑥𝑥
. Find an expression for 𝑓𝑓
𝑔𝑔
𝑥𝑥
A.
𝑥𝑥
2
+
6𝑥𝑥
+ 5
𝑥𝑥
2
B.
𝑥𝑥
2
+
𝑥𝑥
−
1 𝑥𝑥
2
C.
−
3
𝑥𝑥
2
− 2𝑥𝑥 −
3
𝑥𝑥
2
D.
𝑥𝑥
2
+ 5 𝑥𝑥
2
2.
The table gives values for the functions 𝑓𝑓
and 𝑔𝑔
at selected values of 𝑥𝑥
. Functions 𝑓𝑓
and 𝑔𝑔
are defined for all real numbers. Let ℎ
be the function defined by ℎ
𝑥𝑥
=
𝑓𝑓
𝑔𝑔
𝑥𝑥
. What is the value of ℎ
(0)
?
A.
−
4
B.
−
3
C.
1
D.
3
𝒙𝒙
−
2
−
1
0
1
2
𝒇𝒇
(
𝒙𝒙
)
5
3
0
−
2
−
4
𝒈𝒈
(
𝒙𝒙
)
−
3
0
2
−
1
1
3.
The function 𝑔𝑔
is given by 𝑔𝑔
𝑥𝑥
= 4
�
49
𝑥𝑥
. Which of the following is an equivalent form for 𝑔𝑔
(
𝑥𝑥
)
?
A.
𝑔𝑔
𝑥𝑥
= 2
�
7
(
𝑥𝑥
/
2
)
B.
𝑔𝑔
𝑥𝑥
= 2
�
7
(
2𝑥𝑥
)
C.
𝑔𝑔
𝑥𝑥
= 4
�
7
(
𝑥𝑥
/
2
)
D.
𝑔𝑔
𝑥𝑥
= 4
�
7
(
2𝑥𝑥
)
© 2023 Jean Adams Flamingo Math.com 5.
The increasing function 𝑃𝑃
gives the number of followers, in thousands, for an influencer on a social media platform. The table gives the values of 𝑃𝑃
(
𝑡𝑡
)
for selected values of 𝑡𝑡
, in weeks, since the influencer created their account on the social media site. Which of the following models would best represent these data for the scenario?
A.
𝑦𝑦
=
9𝑡𝑡
+ 18
B.
𝑦𝑦
=
235
16
𝑡𝑡
+ 18
C.
𝑦𝑦
= 18
3
2
𝑡𝑡
D.
𝑦𝑦
= 18
2
3
𝑡𝑡
𝒕𝒕
(weeks)
0
1
2
3
4
𝑷𝑷
(
𝒕𝒕
)
(thousands)
18
27
40.5
60.75
91.125
4.
The functions 𝑓𝑓
and 𝑔𝑔
are defined for all real numbers such that 𝑔𝑔
𝑥𝑥
=
𝑓𝑓
3
𝑥𝑥 −
2
. Which of the following sequences of transformations maps the graph of 𝑓𝑓
to the graph of 𝑔𝑔
in the 𝑥𝑥𝑦𝑦 −
plane?
A.
Horizontal dilation of the graph of 𝑓𝑓
by a factor of 1
3
, followed by a horizontal translation of 𝑓𝑓
by 2 units to the right.
B.
Horizontal dilation of the graph of 𝑓𝑓
by a factor of 1
3
, followed by a horizontal translation of 𝑓𝑓
by 2 units to the left.
C.
Horizontal dilation of the graph of 𝑓𝑓
by a factor of 3
, followed by a horizontal translation of 𝑓𝑓
by 2
units to the right.
D.
Horizontal dilation of the graph of 𝑓𝑓
by a factor of 3
, followed by a horizontal translation of 𝑓𝑓
by 2
units to the left.
© 2023 Jean Adams Flamingo Math.com Unit 2
2.4 – 2.7 Quiz
Form A
6.
The value, in millions of dollars, for sales of LVT (luxury vinyl tile) flooring from a distributor is modeled by the function 𝐹𝐹
. The value is expected to increase by 3.2% each quarter of a year. At time 𝑡𝑡
= 0 years, 37 million dollars of sales were processed. If 𝑡𝑡
is measured in years, which of the following is an equation for 𝐹𝐹
(
𝑡𝑡
)
? [Note: A quarter represents one fourth of a year.]
A.
𝐹𝐹
𝑡𝑡
= 37
0.032
𝑡𝑡
/
4
B.
𝐹𝐹
𝑡𝑡
= 37
1.032
4t
C.
𝐹𝐹
𝑡𝑡
= 37
0.032
4𝑡𝑡
D.
𝐹𝐹
𝑡𝑡
= 37
1.032
𝑡𝑡
/
4
8.
The table above presents values for a function 𝑓𝑓
at selected values of 𝑥𝑥
. An exponential regressions 𝑦𝑦
=
𝑎𝑎𝑏𝑏
𝑥𝑥
is used to model these data. What is the value of 𝑓𝑓
(2.5)
predicted by the exponential function model?
A.
65.782
B.
66.234
C.
66.747
D.
66.885
7.
The half-life of morphine in the bloodstream of humans is 3 hours. In a particular patient, the amount of morphine remaining after 𝑡𝑡
hours can be modeled by the function 𝑀𝑀
given by 𝑀𝑀
𝑡𝑡
= 𝐴𝐴
0
0.5
𝑡𝑡
/
3
, where 𝐴𝐴
0
is the initial amount of morphine in the patient at time 𝑡𝑡
= 0
.
If there is 0.4 𝑚𝑚𝑔𝑔
of morphine in the bloodstream, use the equation 𝑀𝑀
to find when the amount of morphine in the bloodstream of the patient drops below 0.01 𝑚𝑚𝑔𝑔
?
A.
𝑡𝑡
= 40
hours
B.
𝑡𝑡
= 20.43
hours
C.
𝑡𝑡
= 15.97
hours
D.
𝑡𝑡
= 6.72
hours
𝒙𝒙
−
3
−
1
1
2
3
𝒇𝒇
(
𝒙𝒙
)
7
14
38
54
82
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