AnswersEAP-Algebra Functions and Data Analysis A CRTransformations of Functions

Transformations of Functions Answers

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

Question illustration
A
y = negative x squared
Option A
B
y = (negative x) squared
Option B
C
y = StartRoot negative x EndRoot
Option C
D
y = negative StartRoot x EndRoot
Option D
2
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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?

Question illustration
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
3

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

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
4

Which of the following is the graph of ?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
5

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

Question illustration
A
y = 2 Superscript x Baseline 3
Option A
B
y = log (2 x) + 3
Option B
C
y = 2 x squared + 2
Option C
D
y = StartFraction 1 Over 2 x EndFraction + 2
Option D
6

Which equation represents the transformed function below?_____ = parent function; - - - - - = transformed function

Question illustration
A
y = log x + 5
Option A
B
y = log x minus 5
Option B
C
y = log (x + 5)
Option C
D
y = log (x minus 5)
Option D
7

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

Question illustration
A
y = x cubed + 4
Option A
B
y = (x + 4) cubed
Option B
C
y = 4 x cubed
Option C
D
y = x Superscript 4
Option D
8

The velocity of a particle can be modeled by the function . Which graph accurately shows the velocity of the particle at any time, t?

Question illustration
A
On a coordinate plane, the x-axis is labeled time and the y-axis is labeled velocity. A cubic root function approaches x = negative 4 in quadrant 3, has a point of inflection at (negative 2.5, negative 2), and then increases into quadrant 2 and approaches x = negative 1.
Option A
B
On a coordinate plane, the x-axis is labeled time and the y-axis is labeled velocity. A cubic root function approaches x = 1 in quadrant 1, has a point of inflection at (2.5, negative 2), and then increases into quadrant 1 and approaches x = 4.
Option B
C
On a coordinate plane, the x-axis is labeled time and the y-axis is labeled velocity. A cubic root function approaches x = 1 in quadrant 1, has a point of inflection at (2.5, 2), and then decreases into quadrant 4 and approaches x = 5.
Option C
D
On a coordinate plane, the x-axis is labeled time and the y-axis is labeled velocity. A cubic root function starts in quadrant 4 and increases into quadrant 1. It has a point of inflection at (8, 2) and then it continue to increase in quadrant 1.
Option D
9

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

Question illustration
A
y = StartAbsoluteValue one-fourth x EndAbsoluteValue
Option A
B
y = StartAbsoluteValue 2 x EndAbsoluteValue
Option B
C
y = StartAbsoluteValue 4 x EndAbsoluteValue
Option C
D
y = StartAbsoluteValue one-half x EndAbsoluteValue
Option D
10

The function models the cost per student of a field trip when x students go on the trip. How is the parent function transformed to create the function ?

Question illustration
A
It is vertically stretched by a factor of 200.
B
It is vertically stretched by a factor of 200 and shifted 10 units left.
C
It is vertically stretched by a factor of 200 and shifted 10 units up.
D
It is vertically stretched by a factor of 200 and shifted 10 units right.
11

How is the graph of the parent function transformed to create the graph of ?

Question illustration
A
It is horizontally stretched by a factor of 3 and reflected over the y-axis.
B
It is translated 3 units down and reflected over the x-axis.
C
It is horizontally compressed by a factor of 3 and reflected over the x-axis.
D
It is translated 3 units down and reflected over the y-axis.
12

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

Question illustration
A
y = negative 2 x cubed
Option A
B
y = negative 6 x cubed
Option B
C
y = 2 x cubed
Option C
D
y = 6 x cubed
Option D
13

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

Question illustration
A
y = StartAbsoluteValue x minus 3 EndAbsoluteValue + 2
Option A
B
y = StartAbsoluteValue x + 3 EndAbsoluteValue minus 2
Option B
C
y = StartAbsoluteValue x minus 2 EndAbsoluteValue + 3
Option C
D
y = StartAbsoluteValue x + 2 EndAbsoluteValue minus 3
Option D
14

To which family does the function belong?

Question illustration
A
quadratic
B
square root
C
exponential
D
reciprocal
15

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

Question illustration
A
It is translated horizontally by 2 units and reflected over the x-axis.
B
It is translated horizontally by 2 units and reflected over the y-axis.
C
It is horizontally compressed by a factor of 2 and reflected over the x-axis.
D
It is horizontally compressed by a factor of 2 and reflected over the y-axis.
16

Which results only in a horizontal compression of by a factor of 6?

Question illustration
A
y = StartFraction 1 Over 6 x EndFraction
Option A
B
y = negative StartFraction 1 Over 6 x EndFraction
Option B
C
y = StartFraction 6 Over x EndFraction
Option C
D
y = negative StartFraction 6 Over x EndFraction
Option D
17

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

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
18

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

Question illustration
A
It is horizontally stretched by a factor of .
Option A
B
It is vertically stretched by a factor of .
Option B
C
It is translated left by unit.
Option C
D
It is translated right by unit.
Option D
19

Which graph is an example of a cubic function?

A
On a coordinate plane, a parabola is shown.
Option A
B
On a coordinate plane, a curve approaches x = negative 2 in quadrant 3, increases to a put of inflection at (0, 1), and then increases again and approaches x = 2.
Option B
C
On a coordinate plane, a straight line has a positive slope.
Option C
D
On a coordinate plane, a function has a line with positive slope that intersects with a line with a negative slope.
Option D
20

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

Question illustration
A
y = StartAbsoluteValue one-fourth x EndAbsoluteValue
Option A
B
y = StartAbsoluteValue 2 x EndAbsoluteValue
Option B
C
y = StartAbsoluteValue 4 x EndAbsoluteValue
Option C
D
y = StartAbsoluteValue one-half x EndAbsoluteValue
Option D

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