Answers SS4 PGCPS ALGEBRA 2 OC SUMMER 2027 - 793033Transformations of Functions

Transformations of Functions Answers

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The graph of a quadratic function, , is reflected over the x-axis. Which of the following is the equation of the transformed graph?

y = negative x squared

y = (negative x) squared

y = StartRoot negative x EndRoot

y = negative StartRoot x EndRoot

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

It is horizontally stretched by a factor of 3 and reflected over the y-axis.

It is translated 3 units down and reflected over the x-axis.

It is horizontally compressed by a factor of 3 and reflected over the x-axis.

It is translated 3 units down and reflected over the y-axis.

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

y = negative 2 x cubed

y = negative 6 x cubed

y = 2 x cubed

y = 6 x cubed

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?

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).

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).

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.

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).

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

y = StartAbsoluteValue x minus 3 EndAbsoluteValue + 2

y = StartAbsoluteValue x + 3 EndAbsoluteValue minus 2

y = StartAbsoluteValue x minus 2 EndAbsoluteValue + 3

y = StartAbsoluteValue x + 2 EndAbsoluteValue minus 3

To which family does the function belong?

quadratic

square root

exponential

reciprocal

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

Option

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

It is translated horizontally by 2 units and reflected over the x-axis.

It is translated horizontally by 2 units and reflected over the y-axis.

It is horizontally compressed by a factor of 2 and reflected over the x-axis.

It is horizontally compressed by a factor of 2 and reflected over the y-axis.

Which results only in a horizontal compression of by a factor of 6?

y = StartFraction 1 Over 6 x EndFraction

y = negative StartFraction 1 Over 6 x EndFraction

y = StartFraction 6 Over x EndFraction

y = negative StartFraction 6 Over x EndFraction

Which of the following is the graph of ?

Option

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

Option

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

It is horizontally stretched by a factor of .

It is vertically stretched by a factor of .

It is translated left by unit.

It is translated right by unit.

Based on the family the graph below belongs to, which equation could represent the graph?

y = 2 Superscript x Baseline 3

y = log (2 x) + 3

y = 2 x squared + 2

y = StartFraction 1 Over 2 x EndFraction + 2

Which graph is an example of a cubic function?

On a coordinate plane, a parabola is shown.

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.

On a coordinate plane, a straight line has a positive slope.

On a coordinate plane, a function has a line with positive slope that intersects with a line with a negative slope.

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

y = StartAbsoluteValue one-fourth x EndAbsoluteValue

y = StartAbsoluteValue 2 x EndAbsoluteValue

y = StartAbsoluteValue 4 x EndAbsoluteValue

y = StartAbsoluteValue one-half x EndAbsoluteValue

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

y = log x + 5

y = log x minus 5

y = log (x + 5)

y = log (x minus 5)

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

The graph is compressed horizontally by a factor of 2, shifted left 3 units, reflected over the x-axis, and translated up 3 units.

The graph is reflected over the x-axis, compressed horizontally by a factor of 2, shifted left 6 units, and translated up 3 units.

The graph is stretched horizontally by a factor of 2, reflected over the x-axis, shifted left 3 units, and translated up 3 units.

The graph is reflected over the x axis, stretched horizontally by a factor of 2, shifted left 6 units, and translated up 3 units.

Based on the family the graph below belongs to, which equation could represent the graph?

y = 0.6 Superscript x Baseline minus 2

y = 0.6 x squared minus 1

y = negative 0.6 x cubed minus 1

y = log (x) minus 2

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

y = x cubed + 4

y = (x + 4) cubed

y = 4 x cubed

y = x Superscript 4

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

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.

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.

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.

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.

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

The graph is compressed horizontally by a factor of 2, shifted left 3 units, reflected over the x-axis, and translated up 3 units.

The graph is reflected over the x-axis, compressed horizontally by a factor of 2, shifted left 6 units, and translated up 3 units.

The graph is stretched horizontally by a factor of 2, reflected over the x-axis, shifted left 3 units, and translated up 3 units.

The graph is reflected over the x axis, stretched horizontally by a factor of 2, shifted left 6 units, and translated up 3 units.

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

y = StartAbsoluteValue one-fourth x EndAbsoluteValue

y = StartAbsoluteValue 2 x EndAbsoluteValue

y = StartAbsoluteValue 4 x EndAbsoluteValue

y = StartAbsoluteValue one-half x EndAbsoluteValue

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

It is translated 1 unit right and compressed vertically by a factor of 3.

It is translated 1 unit left and compressed vertically by a factor of 3.

It is translated 1 unit right and stretched vertically by a factor of 3.

It is translated 1 unit left and stretched vertically by a factor of 3.

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 ?

It is vertically stretched by a factor of 200.

It is vertically stretched by a factor of 200 and shifted 10 units left.

It is vertically stretched by a factor of 200 and shifted 10 units up.

It is vertically stretched by a factor of 200 and shifted 10 units right.

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