Answers High School Math 2 ALinear Growth vs. Exponential Growth

Transformations of Functions Answers

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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.

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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 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.

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 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 the function is shown.Which graph represents the function ?

On a coordinate plane, 2 curves have an asymptote at y = 0. One curve opens up and to the right in quadrant 1 and goes through (1, 2) and (2, 1). The other curve opens down and to the left in quadrant 3 and goes through (negative 2, negative 1) and (negative 1, negative 2).

On a coordinate plane, 2 curves have an asymptote at y = 0. One curve opens up and to the right in quadrant 1 and goes through (2, 2.5). The other curve opens down and to the left in quadrants 2 and 3 and goes through (negative 0.5, 0) and (negative 2, 1.5).

On a coordinate plane, 2 curves have an asymptote at y = negative 2. On curve opens up and to the right in quadrants 1 and 2 and goes through (negative 1, 1) and (0, 0.5). Another curve opens down and to the right in quadrant 3 and goes through (negative 3, negative 1) and (negative 2.5, negative 2).

On a coordinate plane, 2 curves have an asymptote at y = 0. One curve opens up and to the right in quadrant 1 and goes through (0.5, 1) and (1, 0.5). The other curve opens down and to the left in quadrant 3 and goes through (negative 1, negative 0.5) and (negative 0.5, negative 0.5).

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

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 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)

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).

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Transformations of Functions Answers

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