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Feb 20, 2024
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© 2023 Jean Adams Flamingo Math.com Unit 2
2.4 – 2.7 Quiz
Form A
1.
The function ࠵࠵?
is given by ࠵࠵?
࠵࠵?
=
࠵࠵?
2
−
4
and the function ࠵࠵?
is given by ࠵࠵?
࠵࠵?
=
࠵࠵?+3
࠵࠵?
. Find an expression for ࠵࠵?
࠵࠵?
࠵࠵?
A.
࠵࠵?
2
+
6࠵࠵?
+ 5
࠵࠵?
2
B.
࠵࠵?
2
+
࠵࠵?
−
1 ࠵࠵?
2
C.
−
3
࠵࠵?
2
− 2࠵࠵? −
3
࠵࠵?
2
D.
࠵࠵?
2
+ 5 ࠵࠵?
2
2.
The table gives values for the functions ࠵࠵?
and ࠵࠵?
at selected values of ࠵࠵?
. Functions ࠵࠵?
and ࠵࠵?
are defined for all real numbers. Let ℎ
be the function defined by ℎ
࠵࠵?
=
࠵࠵?
࠵࠵?
࠵࠵?
. What is the value of ℎ
(0)
?
A.
−
4
B.
−
3
C.
1
D.
3
࠵ಙ࠵?
−
2
−
1
0
1
2
࠵ಇ࠵?
(
࠵ಙ࠵?
)
5
3
0
−
2
−
4
࠵ಈ࠵?
(
࠵ಙ࠵?
)
−
3
0
2
−
1
1
3.
The function ࠵࠵?
is given by ࠵࠵?
࠵࠵?
= 4
�
49
࠵࠵?
. Which of the following is an equivalent form for ࠵࠵?
(
࠵࠵?
)
?
A.
࠵࠵?
࠵࠵?
= 2
�
7
(
࠵࠵?
/
2
)
B.
࠵࠵?
࠵࠵?
= 2
�
7
(
2࠵࠵?
)
C.
࠵࠵?
࠵࠵?
= 4
�
7
(
࠵࠵?
/
2
)
D.
࠵࠵?
࠵࠵?
= 4
�
7
(
2࠵࠵?
)
© 2023 Jean Adams Flamingo Math.com 5.
The increasing function ࠵ృ࠵?
gives the number of followers, in thousands, for an influencer on a social media platform. The table gives the values of ࠵ృ࠵?
(
࠵ౡ࠵?
)
for selected values of ࠵ౡ࠵?
, 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.
࠵౦࠵?
=
9࠵ౡ࠵?
+ 18
B.
࠵౦࠵?
=
235
16
࠵ౡ࠵?
+ 18
C.
࠵౦࠵?
= 18
3
2
࠵ౡ࠵?
D.
࠵౦࠵?
= 18
2
3
࠵ౡ࠵?
࠵ಕ࠵?
(weeks)
0
1
2
3
4
࠵౷࠵?
(
࠵ಕ࠵?
)
(thousands)
18
27
40.5
60.75
91.125
4.
The functions ࠵࠵?
and ࠵࠵?
are defined for all real numbers such that ࠵࠵?
࠵࠵?
=
࠵࠵?
3
࠵࠵? −
2
. Which of the following sequences of transformations maps the graph of ࠵࠵?
to the graph of ࠵࠵?
in the ࠵࠵?࠵౦࠵? −
plane?
A.
Horizontal dilation of the graph of ࠵࠵?
by a factor of 1
3
, followed by a horizontal translation of ࠵࠵?
by 2 units to the right.
B.
Horizontal dilation of the graph of ࠵࠵?
by a factor of 1
3
, followed by a horizontal translation of ࠵࠵?
by 2 units to the left.
C.
Horizontal dilation of the graph of ࠵࠵?
by a factor of 3
, followed by a horizontal translation of ࠵࠵?
by 2
units to the right.
D.
Horizontal dilation of the graph of ࠵࠵?
by a factor of 3
, followed by a horizontal translation of ࠵࠵?
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 ࠵హ࠵?
. The value is expected to increase by 3.2% each quarter of a year. At time ࠵ౡ࠵?
= 0 years, 37 million dollars of sales were processed. If ࠵ౡ࠵?
is measured in years, which of the following is an equation for ࠵హ࠵?
(
࠵ౡ࠵?
)
? [Note: A quarter represents one fourth of a year.]
A.
࠵హ࠵?
࠵ౡ࠵?
= 37
0.032
࠵ౡ࠵?
/
4
B.
࠵హ࠵?
࠵ౡ࠵?
= 37
1.032
4t
C.
࠵హ࠵?
࠵ౡ࠵?
= 37
0.032
4࠵ౡ࠵?
D.
࠵హ࠵?
࠵ౡ࠵?
= 37
1.032
࠵ౡ࠵?
/
4
8.
The table above presents values for a function ࠵࠵?
at selected values of ࠵࠵?
. An exponential regressions ࠵౦࠵?
=
࠵࠵?࠵࠵?
࠵࠵?
is used to model these data. What is the value of ࠵࠵?
(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 ࠵ౡ࠵?
hours can be modeled by the function ࠵ీ࠵?
given by ࠵ీ࠵?
࠵ౡ࠵?
= ࠵ఴ࠵?
0
0.5
࠵ౡ࠵?
/
3
, where ࠵ఴ࠵?
0
is the initial amount of morphine in the patient at time ࠵ౡ࠵?
= 0
.
If there is 0.4 ࠵ౚ࠵?࠵࠵?
of morphine in the bloodstream, use the equation ࠵ీ࠵?
to find when the amount of morphine in the bloodstream of the patient drops below 0.01 ࠵ౚ࠵?࠵࠵?
?
A.
࠵ౡ࠵?
= 40
hours
B.
࠵ౡ࠵?
= 20.43
hours
C.
࠵ౡ࠵?
= 15.97
hours
D.
࠵ౡ࠵?
= 6.72
hours
࠵ಙ࠵?
−
3
−
1
1
2
3
࠵ಇ࠵?
(
࠵ಙ࠵?
)
7
14
38
54
82
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