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Transformations of Functions Answers

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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
2
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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.
3

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
4

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
5

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
6

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
7

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

Question illustration
A
The graph is compressed horizontally by a factor of 2, shifted left 3 units, reflected over the x-axis, and translated up 3 units.
B
The graph is reflected over the x-axis, compressed horizontally by a factor of 2, shifted left 6 units, and translated up 3 units.
C
The graph is stretched horizontally by a factor of 2, reflected over the x-axis, shifted left 3 units, and translated up 3 units.
D
The graph is reflected over the x axis, stretched horizontally by a factor of 2, shifted left 6 units, and translated up 3 units.
8

To which family does the function belong?

Question illustration
A
quadratic
B
square root
C
exponential
D
reciprocal
9

The graph below belongs to which function family?

Question illustration
A
linear
B
quadratic
C
cubic
D
absolute value
10

Which graph is an example of a function whose parent function is ?

Question illustration
A
On a coordinate plane, a curve starts at (negative 1, negative 1) and then curves up and to the right into quadrant 1.
Option A
B
On a coordinate plane, a parabola has a vertex at (0, 1).
Option B
C
On a coordinate plane, 2 curves are shown. Both curves have an asymptote at x = negative 1. One curved decreases from quadrant 2 into quadrant 1 and approaches y = 1. It crosses the y-axis at (0, 2). The other curve approaches y = 1 in quadrant 1 and then curves down and approaches y = negative 1 in quadrant 3. It crosses the x-axis at (negative 2, 0).
Option C
D
On a coordinate plane, a curve starts in quadrant 3 and then increases into quadrant 1. It crosses the y-axis at (0, negative 2) and crosses the x-axis at (1.5, 0).
Option D

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