Answers2026-2027_MDCPS_1200330_Algebra 2_FYTransformations of Functions

Transformations of Functions Answers

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1
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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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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
3

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
4

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

Question illustration
I
It is translated 1 unit right and compressed vertically by a factor of 3.
I
It is translated 1 unit left and compressed vertically by a factor of 3.
I
It is translated 1 unit right and stretched vertically by a factor of 3.
I
It is translated 1 unit left and stretched vertically by a factor of 3.
5

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

Question illustration
A
On a coordinate plane, a cubic root function is shown. It approaches x = negative 3 in quadrant 3, has an inflection point at (negative 1, negative 2), and then approaches y = 2 in quadrant 1. It crosses the y-axis at (0, negative 2).
Option A
B
On a coordinate plane, a cubic root function is shown. It approaches x = negative 1 in quadrant 3, has an inflection point at (2, 1), and then increases and approaches y = 5.
Option B
C
On a coordinate plane, a cubic root function is shown. It approaches the y-axis in quadrant 4, increases, has a point of inflection at (2, 1), and then increases and approaches x = 4.
Option C
D
On a coordinate plane, a cubic root function is shown. It approaches the y-axis in quadrant 2, decreases, has a point of inflection at (negative 2, 1), and then decreases and approaches x = negative 4.
Option D
6

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
7

To which family does the function belong?

Question illustration
q
quadratic
s
square root
e
exponential
l
logarithmic
8

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

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
9

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
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

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