AnswersSS4 PGCPS ALGEBRA 2 OC SUMMER 2027 - 793033Transformations of Functions

Transformations of Functions Answers

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1
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The graph below belongs to which function family?

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A
linear
B
quadratic
C
cubic
D
absolute value
2
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Based on the family the graph below belongs to, which equation could represent the graph?

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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
3

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?

Question illustration
A
y = (one-fifth x) cubed
Option A
B
y = (negative one-fifth x) cubed
Option B
C
y = (5 x) cubed
Option C
D
y = (negative 5 x) cubed
Option D
4

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

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

Question illustration
A
y = 0.6 Superscript x Baseline minus 2
Option A
B
y = 0.6 x squared minus 1
Option B
C
y = negative 0.6 x cubed minus 1
Option C
D
y = log (x) minus 2
Option D
6

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
7

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
8

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
9

The graph of the function is shown.Which graph represents the function ?

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A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
10

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
14

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

Question illustration
A
y = StartRoot x + 2 EndRoot
Option A
B
y = StartRoot x EndRoot + 2
Option B
C
y = StartRoot x EndRoot minus 2
Option C
D
y = StartRoot x minus 2 EndRoot
Option D
15

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
21

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
28

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
32

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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