AnswersAlgebra 2 MP 234 CHSGraphing Sine and Cosine

Transformations of Functions Answers

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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
2
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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.
3

To which family does the function belong?

Question illustration
A
quadratic
B
square root
C
exponential
D
reciprocal
4

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

Question illustration
A
It is horizontally stretched by a factor of 3 and reflected over the y-axis.
B
It is translated 3 units down and reflected over the x-axis.
C
It is horizontally compressed by a factor of 3 and reflected over the x-axis.
D
It is translated 3 units down and reflected over the y-axis.
5

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
6

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
7

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
8

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
9

The function models the cost per student of a field trip when x students go on the trip. How is the parent function transformed to create the function ?

Question illustration
A
It is vertically stretched by a factor of 200.
B
It is vertically stretched by a factor of 200 and shifted 10 units left.
C
It is vertically stretched by a factor of 200 and shifted 10 units up.
D
It is vertically stretched by a factor of 200 and shifted 10 units right.
10

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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