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Transformations of Functions Answers

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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
2
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How is the graph of the parent function of transformed to produce the graph ?

Question illustration
A
It is horizontally stretched by a factor of .
Option A
B
It is vertically stretched by a factor of .
Option B
C
It is translated left by unit.
Option C
D
It is translated right by unit.
Option D
3

The graph of is transformed as shown in the graph below. Which equation represents the transformed function?

Question illustration
A
y = StartAbsoluteValue one-fourth x EndAbsoluteValue
Option A
B
y = StartAbsoluteValue 2 x EndAbsoluteValue
Option B
C
y = StartAbsoluteValue 4 x EndAbsoluteValue
Option C
D
y = StartAbsoluteValue one-half x EndAbsoluteValue
Option D
4

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
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

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
I
It is a vertical stretch with a factor of 100 and a translation 5 units right.
I
It is a vertical stretch with a factor of 95.
I
It is a vertical stretch with a factor of 100 and a translation 5 units down.
I
It is a vertical stretch with a factor of 500.
7

The velocity of a particle can be modeled by the function . Which graph accurately shows the velocity of the particle at any time, t?

Question illustration
A
On a coordinate plane, the x-axis is labeled time and the y-axis is labeled velocity. A cubic root function approaches x = negative 4 in quadrant 3, has a point of inflection at (negative 2.5, negative 2), and then increases into quadrant 2 and approaches x = negative 1.
Option A
B
On a coordinate plane, the x-axis is labeled time and the y-axis is labeled velocity. A cubic root function approaches x = 1 in quadrant 1, has a point of inflection at (2.5, negative 2), and then increases into quadrant 1 and approaches x = 4.
Option B
C
On a coordinate plane, the x-axis is labeled time and the y-axis is labeled velocity. A cubic root function approaches x = 1 in quadrant 1, has a point of inflection at (2.5, 2), and then decreases into quadrant 4 and approaches x = 5.
Option C
D
On a coordinate plane, the x-axis is labeled time and the y-axis is labeled velocity. A cubic root function starts in quadrant 4 and increases into quadrant 1. It has a point of inflection at (8, 2) and then it continue to increase in quadrant 1.
Option D
8

Which of the following is the graph of ?

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

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
10

Which equation describes how the parent function, , is vertically stretched by a factor of 4?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
11

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
12

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.
13

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
14

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

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