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

Transformations of Functions Answers

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The graph of the function is shown.Which graph represents the function ?

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For which graph is the parent function ?

On a coordinate plane, a parabola opens up and has a vertex at (negative 1, negative 2).

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

On a coordinate plane, a cubic root function is shown.

On a coordinate plane, an absolute value function is shown.

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 of the following is the graph of ?

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Which graph is an example of a function whose parent function is ?

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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

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.

Which is the graph of ?

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).

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).

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).

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).

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 shown.Which is the graph of ?

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).

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.

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.

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.

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.

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.

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 ?