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.
11

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
12

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
13

The value of a graphed function doubles for each increase of 1 in the value of x. Which of the following could be the parent function of the graphed function?

A
y = 2 Superscript x
Option A
B
y = x squared
Option B
C
y = StartAbsoluteValue x EndAbsoluteValue
Option C
D
y = StartRoot x EndRoot
Option D
14

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
15

Which of the following is the graph of ?

Question illustration
A
On a coordinate plane, a cubic root function approaches the negative y-axis in quadrant 4, has a point of inflection at (2, negative 5), and then increases and approaches x = 4.
Option A
B
On a coordinate plane, a cubic root function approaches x = negative 5 in quadrant 3, has a point of inflection at (negative 2, negative 5), and then approaches the y-axis in quadrant 3.
Option B
C
On a coordinate plane, a cubic root function approaches the y-axis in quadrant 4, has a point of inflection at (2, negative 5), and then decreases and approaches x = 4.
Option C
D
On a coordinate plane, a cubic root function approaches x = negative 4 in quadrant 3, has a point of inflection at (negative 2, negative 5), and then decreases and approaches the negative y-axis in quadrant 3.
Option D
16

Which is the graph of ?

Question illustration
A
On a coordinate plane, a curve opens down and to the right and approaches y = 0 in quadrant 4. It increases into quadrant 1 and goes through (1, 3) and (4, 6).
Option A
B
On a coordinate plane, a curve opens down and to the right and approaches y = negative 3 in quadrant 3. It increases into quadrant 1 and goes through (negative 2, 0) and (1, 3).
Option B
C
On a coordinate plane, a curve approaches x = negative 3 in quadrant 4 and increases into quadrant 1. It goes through (4, 0) and (7, 3).
Option C
D
On a coordinate plane, a curve approaches y = 0 in quadrant 4 and then increases into quadrant 1. It goes through (4, 0) and (6, 1).
Option D
17

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
18

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
19

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

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