Transformations of Functions Answers

1

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The graph below belongs to which function family?

A

linear

B

quadratic

C

cubic

D

absolute value

1

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For which graph is the parent function ?

A

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

B

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

C

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

D

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

1

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

A

y = negative 2 x cubed

B

y = negative 6 x cubed

C

y = 2 x cubed

D

y = 6 x cubed

2

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

A

y = 2 Superscript x Baseline 3

B

y = log (2 x) + 3

C

y = 2 x squared + 2

D

y = StartFraction 1 Over 2 x EndFraction + 2

2

Which graph is an example of a cubic function?

A

On a coordinate plane, a parabola is shown.

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.

C

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

D

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

3

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?

A

y = (one-fifth x) cubed

B

y = (negative one-fifth x) cubed

C

y = (5 x) cubed

D

y = (negative 5 x) cubed

3

To which family does the function belong?

A

quadratic

B

square root

C

exponential

D

logarithmic

4

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 ?

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.

4

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?

A

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).

B

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).

C

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.

D

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).

5

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

A

y = 0.6 Superscript x Baseline minus 2

B

y = 0.6 x squared minus 1

C

y = negative 0.6 x cubed minus 1

D

y = log (x) minus 2

5

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

A

y = StartAbsoluteValue x minus 3 EndAbsoluteValue + 2

B

y = StartAbsoluteValue x + 3 EndAbsoluteValue minus 2

C

y = StartAbsoluteValue x minus 2 EndAbsoluteValue + 3

D

y = StartAbsoluteValue x + 2 EndAbsoluteValue minus 3

6

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

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.

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.

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.

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.

6

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

A

y = 0.6 Superscript x Baseline minus 2

B

y = 0.6 x squared minus 1

C

y = negative 0.6 x cubed minus 1

D

y = log (x) minus 2

7

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?

A

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).

B

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).

C

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.

D

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).

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?

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.

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.

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.

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.

8

Which graph is an example of a cubic function?

A

On a coordinate plane, a parabola is shown.

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.

C

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

D

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

9

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