Answers Academy - Algebra Functions and Data AnalysisUnit Test

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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.

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

Option

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 ?

It is a vertical stretch with a factor of 100 and a translation 5 units right.

It is a vertical stretch with a factor of 95.

It is a vertical stretch with a factor of 100 and a translation 5 units down.

It is a vertical stretch with a factor of 500.

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

Option

To which family does the function belong?

quadratic

square root

exponential

logarithmic

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.

Which of the following is the graph of ?

Option

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

On a coordinate plane, a curve starts at (negative 1, negative 1) and then curves up and to the right into quadrant 1.

On a coordinate plane, a parabola has a vertex at (0, 1).

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).

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).

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

Option

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

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

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?

y = (one-fifth x) cubed

y = (negative one-fifth x) cubed

y = (5 x) cubed

y = (negative 5 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).