AnswersSS4 PGCPS ALGEBRA 2 OC SUMMER 2027 - 793033Transformations of Functions

Transformations of Functions Answers

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Which of the following is the graph of ?

Question illustration
A
On a coordinate plane, a cubic root function approaches the negative y-axis in quadrant 4, has a point of inflection at (2, negative 5), and then increases and approaches x = 4.
Option A
B
On a coordinate plane, a cubic root function approaches x = negative 5 in quadrant 3, has a point of inflection at (negative 2, negative 5), and then approaches the y-axis in quadrant 3.
Option B
C
On a coordinate plane, a cubic root function approaches the y-axis in quadrant 4, has a point of inflection at (2, negative 5), and then decreases and approaches x = 4.
Option C
D
On a coordinate plane, a cubic root function approaches x = negative 4 in quadrant 3, has a point of inflection at (negative 2, negative 5), and then decreases and approaches the negative y-axis in quadrant 3.
Option D
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The graph of is transformed as shown in the graph below. Which equation represents the transformed function?

Question illustration
A
y = StartAbsoluteValue x minus 3 EndAbsoluteValue + 2
Option A
B
y = StartAbsoluteValue x + 3 EndAbsoluteValue minus 2
Option B
C
y = StartAbsoluteValue x minus 2 EndAbsoluteValue + 3
Option C
D
y = StartAbsoluteValue x + 2 EndAbsoluteValue minus 3
Option D
3

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
4

To which family does the function belong?

Question illustration
A
quadratic
B
square root
C
exponential
D
reciprocal
5

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
6

Which equation represents the transformed function below?_____ = parent function; - - - - - = transformed function

Question illustration
A
y = StartRoot x + 2 EndRoot
Option A
B
y = StartRoot x EndRoot + 2
Option B
C
y = StartRoot x EndRoot minus 2
Option C
D
y = StartRoot x minus 2 EndRoot
Option D
7

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
8

To which family does the function belong?

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

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
10

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

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