Answers2026-2027_MDCPS_1200330_Algebra 2_FYComparing Characteristics of Functions

Transformations of Functions Answers

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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.
2
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For which graph is the parent function ?

Question illustration
A
On a coordinate plane, a parabola opens up and has a vertex at (negative 1, negative 2).
Option A
B
On a coordinate plane, a straight line has a positive slope.
Option B
C
On a coordinate plane, a cubic root function is shown.
Option C
D
On a coordinate plane, an absolute value function is shown.
Option D
3

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

Question illustration
A
It is translated 1 unit right and compressed vertically by a factor of 3.
B
It is translated 1 unit left and compressed vertically by a factor of 3.
C
It is translated 1 unit right and stretched vertically by a factor of 3.
D
It is translated 1 unit left and stretched vertically by a factor of 3.
4

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
5

The graph below belongs to which function family?

Question illustration
A
linear
B
quadratic
C
cubic
D
absolute value
6

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
7

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
8

To which family does the function belong?

Question illustration
A
quadratic
B
square root
C
exponential
D
logarithmic
10

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 ?

Question illustration
A
It is a vertical stretch with a factor of 100 and a translation 5 units right.
B
It is a vertical stretch with a factor of 95.
C
It is a vertical stretch with a factor of 100 and a translation 5 units down.
D
It is a vertical stretch with a factor of 500.

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