AnswersAcademy - Algebra Functions and Data AnalysisUnit Test

Unit Test Answers

14 verified answers
1
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How is the graph of the parent function transformed to produce the graph of ?

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It is translated 1 unit right and compressed vertically by a factor of 3.
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It is translated 1 unit left and compressed vertically by a factor of 3.
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It is translated 1 unit right and stretched vertically by a factor of 3.
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It is translated 1 unit left and stretched vertically by a factor of 3.
2
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The graph of the function is shown.Which graph represents the function ?

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3

A 100-gallon fish tank fills at a rate of x gallons per minute. The tank has already been filling for 5 minutes. The function represents the remaining time in minutes needed to fill the tank. How is the graph of the parent function transformed to create the graph of the function ?

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It is a vertical stretch with a factor of 100 and a translation 5 units right.
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It is a vertical stretch with a factor of 95.
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It is a vertical stretch with a factor of 100 and a translation 5 units down.
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It is a vertical stretch with a factor of 500.
4

Based on the family the graph below belongs to, which equation could represent the graph?

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y = 2 Superscript x Baseline 3
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y = log (2 x) + 3
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C
y = 2 x squared + 2
Option C
D
y = StartFraction 1 Over 2 x EndFraction + 2
Option D
5

Which equation describes how the parent function, , is vertically stretched by a factor of 4?

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6

To which family does the function belong?

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q
quadratic
s
square root
e
exponential
l
logarithmic
7

How is the graph of the parent quadratic function transformed to produce the graph of ?

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The graph is compressed horizontally by a factor of 2, shifted left 3 units, reflected over the x-axis, and translated up 3 units.
B
The graph is reflected over the x-axis, compressed horizontally by a factor of 2, shifted left 6 units, and translated up 3 units.
C
The graph is stretched horizontally by a factor of 2, reflected over the x-axis, shifted left 3 units, and translated up 3 units.
D
The graph is reflected over the x axis, stretched horizontally by a factor of 2, shifted left 6 units, and translated up 3 units.
8

Which of the following is the graph of ?

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9

Which graph is an example of a function whose parent function is ?

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10

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

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16

The graph of a quadratic function, , is reflected over the x-axis. Which of the following is the equation of the transformed graph?

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y = negative x squared
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y = (negative x) squared
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y = StartRoot negative x EndRoot
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y = negative StartRoot x EndRoot
Option D
21

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

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y = StartAbsoluteValue x minus 3 EndAbsoluteValue + 2
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B
y = StartAbsoluteValue x + 3 EndAbsoluteValue minus 2
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y = StartAbsoluteValue x minus 2 EndAbsoluteValue + 3
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D
y = StartAbsoluteValue x + 2 EndAbsoluteValue minus 3
Option D
30

The graph of the parent function is horizontally stretched by a factor of and reflected over the y-axis. What is the equation of the transformed function?

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y = (one-fifth x) cubed
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y = (negative one-fifth x) cubed
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y = (5 x) cubed
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D
y = (negative 5 x) cubed
Option D
40

An engineer is using a polynomial function to model the height of a roller coaster over time x, as shown. The engineer wants to modify the roller coaster design by transforming the function. Which represents , the modified design of the roller coaster?

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A
On a coordinate plane, a curve increases from quadrant 3 and crosses the y-axis at (0, 10). It then decreases and goes through (20, 10). It continues to decrease and then starts to increase and goes through (30, 10).
Option A
B
On a coordinate plane, a curve increases from quadrant 3 and crosses the y-axis at (0, negative 10). It then decreases and goes through (20, negative 10). It continues to decrease and then starts to increase and goes through (30, negative 10).
Option B
C
On a coordinate plane, a curve increases from quadrant 3 and crosses the y-axis at (0, 20). It then decreases and then increases again.
Option C
D
On a coordinate plane, a curve increases from quadrant 3 and crosses the y-axis at (0, 10). It then decreases and goes through (20, negative 10). It continues to decrease and then starts to increase and goes through (30, negative 10).
Option D

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