AnswersFL-1200330-Algebra 2 AModeling with Functions

Modeling with Functions — Unit test Answers

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The end of a hose was resting on the ground, pointing up an angle. Sal measured the path of the water coming out of the hose and found that it could be modeled using the equation f(x) = –0.3x2 + 2x, where f(x) is the height of the path of the water above the ground, in feet, and x is the horizontal distance of the path of the water from the end of the hose, in feet.

A
3.2 feet
B
4.8 feet
C
5.6 feet
D
6.8 feet
2
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The table shows a company’s profit based on the number of pounds of food produced.

Question illustration
A
$5,150
B
$5,300
C
$10,150
D
$11,000
3

The table shows the approximate height of an object x seconds after the object was dropped. The function h(x) = –16x2 + 100 models the data in the table.

Question illustration
A
–2.75
B
0.25
C
1.75
D
2.25
4

The graph below is an example of which type of function?

Question illustration
A
quadratic
B
linear
C
cubic
D
square root
5

The table below shows the different times it takes Paula to drive to her grandmother’s house depending on the rate at which she drives.Rate vs. TimeRate (mph)30405060Time (h)2.51.8751.51.25If one day Paula rides a scooter to her grandmother’s house at a constant rate of 24 miles per hour, how long should it take her?

A
2.625 hours
B
2.75 hours
C
3.125 hours
D
3.75 hours
6

Which statements can be used to accurately compare the functions? Select two options.

A
g(x) has the lowest minimum.
B
f(x) has the greatest maximum.
C
All three functions have a y-intercept.
D
All three functions have an x-intercept.
E
The domain of all three functions is the same.
7

The graph shows the exponential regression model for data representing a rabbit population after x years.

Question illustration
A
The graph of the regression model is limited to whole-number values for x.
B
The graph of the regression model is limited to whole-number values for y.
C
The graph of the regression model cannot be used to approximate the population size for year 1.
D
The graph of the regression model can be used to predict the population size for any number of years in the future.
8

A customer deposits $1,000 in an account in which the interest is compounded annually. The table below shows the balances in the account at the end of each year.Amount in Account vs. Number of YearsAmount in Account, ANumber of Years After Initial Deposit, t1,00001,08011,166.4021,259.7131,360.494Which equation best represents the data in the table?

A
A = 1000 (1.08) Superscript t
Option A
B
A = 1080 Superscript t
Option B
C
A = 1000 (1.8) Superscript t
Option C
D
A = 800 Superscript t
Option D
9

Consider the functions.f(x) = (x + 1)2 – 4g(x) = –4 |x + 1|

A
The ranges of both f(x) and g(x) are limited to y ≥ –1.
B
The ranges of both f(x) and g(x) are limited to y ≤ –1.
C
Since the range of f(x) is limited to y ≤ 0 and the range of g(x) is limited to y ≥ –4, the ranges overlap for the values –4 ≤ y ≤ 0.
D
Since the range of f(x) is limited to y ≥ –4 and the range of g(x) is limited to y ≤ 0, the ranges overlap for the values –4 ≤ y ≤ 0.
10

The graphs of three functions are shown.

Question illustration
A
All of the functions have a maximum.
B
The square root and quadratic function share a minimum.
C
The absolute value and quadratic function share a y-intercept.
D
The absolute value and square root function share an x-intercept.
11

The table shows the daily pay in dollars, f(x), earned by a salesperson who makes x number of sales.

Question illustration
A
f(x) = 50x2 + 200
B
f(x) = x50 + 200
C
Option
Option C
D
f(x) = 50x + 200
12

The graph of is transformed as shown in the graph below. Which equation represents the transformed function?

Question illustration
A
y = negative StartRoot x EndRoot
Option A
B
y = StartRoot (negative x) EndRoot + 2
Option B
C
y = StartRoot (negative x) EndRoot minus 2
Option C
D
y = negative StartRoot x EndRoot minus 2
Option D
13

Choose the function that represents the data in the table.

Question illustration
A
y = x2
B
y = 3x2
C
y = x2 + 3
D
y = 2x + 3
14

How is the graph of transformed to produce the graph of ?

Question illustration
A
The graph is stretched horizontally by a factor of 2 and then moved right 4 units.
B
The graph is compressed horizontally by a factor of 2 and then moved down 4 units.
C
The graph is compressed horizontally by a factor of 2, moved left 4 units, and moved down 4 units.
D
The graph is stretched horizontally by a factor of 2, moved left 4 units, and moved down 4 units.
15

Which function has the same maximum value as f(x) = – |x + 3| – 2?

A
Option
Option A
B
f(x) = (x + 3)2 – 2
C
Option
Option C
D
f(x) = –(x – 6)2 – 3

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