AnswersEAP-Algebra Functions and Data Analysis A CRTransformations of Functions

Transformations of Functions — Test Answers

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Consider the function f(x) = x3 + 0.5x – 1. Marjan needs to graph f(x) and g(x) = –f(x) – 3. His graphs are shown below.

Question illustration
A
No, the reflection should be over the x-axis, not the y-axis.
B
No, the reflection should be over the y-axis, not the x-axis.
C
Yes, g(x) is a reflection of f(x) over the y-axis followed by a translation of 3 units down.
D
Yes, g(x) is a reflection of f(x) over the x-axis followed by a translation of 3 units down.
22
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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
23

Which transformations to the graph of j(x) would result in the graph of j(4x) – 27?

A
horizontal stretch by a factor of 4, and a translation 27 units right
B
horizontal stretch by a factor of 4, and a translation 27 units down
C
horizontal compression by a factor of , and a translation 27 units right
Option C
D
horizontal compression by a factor of , and a translation 27 units down
Option D
24

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
25

The graph models the projected populations, in thousands, of two towns after x years. Both towns experience a 1.9% annual growth rate.

Question illustration
A
g(x) = f
Option A
B
g(x) = f
Option B
C
g(x) = f(x) +
Option C
D
g (x) = five-thirds times f (x)
Option D
26

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
27

Consider the function m(x) = 2x.Which is the graph of m(x)?

Question illustration
A
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then curves up through (0, 3) and (1, 6) into quadrant 1.
Option A
B
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then curves up through (0, 0.6) and (4, 5) into quadrant 1.
Option B
C
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then curves up through (0, 1) and (1, 7) into quadrant 1.
Option C
D
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then curves up through (0, 1) and (3, 2) into quadrant 1.
Option D
28

Which is the graph of ?

Question illustration
A
On a coordinate plane, a curve starts at (0, 2) and curves up through (30, 5) and (70, 6).
Option A
B
On a coordinate plane, a curve starts at (0, 0) and curves up through (50, 3) and (80, 3.5).
Option B
C
On a coordinate plane, a curve starts at (0, 0) and curves up through (60, 5) and (80, 5.5).
Option C
D
On a coordinate plane, a curve starts at (0, 0) and curves up through (60, 8) and (70, 8.4).
Option D
29

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.
30

Consider the function f(x) = x5 – 3x2 + 5x. Let g(x) = f(–x + 4).Which shows the graphs of f(x) and g(x)?

A
On a coordinate plane, y = f (x) goes through (negative 0.5, negative 3) and (0, 0) to an inflection point around (0.8, 2.6) and then curves up through (1, 3). Y = g (x) goes through (4.5, negative 3) through (4, 0) to an inflection point around (3.3, 2.4) and then curves up through (3, 3).
Option A
B
On a coordinate plane, y = f (x) goes through (negative 0.5, negative 3) and (0, 0) to an inflection point around (0.8, 2.6), and then curves up through (1, 3). Y = g (X) goes through (negative 3.5, negative 3) and (negative 4, 0) to an inflection point around (negative 4.5, 2.4) and curves up through (negative 5, 3).
Option B
C
On a coordinate plane, y = f (x) goes through (negative 0.5, negative 3) and (0, 0) to an inflection point around (0.8, 2.6), and then curves up through (1, 3). Y = g (x) goes through (5, negative 3) to an inflection point around (4.5, negative 2.5) and curves up through 4, 0).
Option C
D
On a coordinate plane, y = f (x) goes through (negative 0.5, negative 3) and (0, 0) to an inflection point around (0.8, 2.6), and then curves up through (1, 3). Y = g (x) goes through (negative 3, negative 3) to an inflection point around (negative 3.2, negative 2.5) and curves up through (negative 4, 0).
Option D
31

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
32

To which family does the function belong?

Question illustration
A
quadratic
B
square root
C
exponential
D
reciprocal
33

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
34

Which is the graph of y = log4(x+3)?

A
On a coordinate plane, a curve starts at (0, 0) and curves up through (1, 3) and goes through (4, 4).
Option A
B
On a coordinate plane, a curve approaches the y-axis in quadrant 4 and increases up through (1, 0.5) and (5, 2).
Option B
C
On a coordinate plane, a curve approaches x = negative 3 and curves up through (negative 2, 0) and goes through (1, 1).
Option C
D
On a coordinate plane, a curve approaches x = 3 and curves up through (4, 0).
Option D

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