Answers 2026-2027_MDCPS_1200330_Algebra 2_FYTransformations of Functions

Transformations of Functions — Test Answers

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Consider the function h(x) = . Which graph shows h(2x) + 4?

On a coordinate plane, a curve opens up and to the right in quadrants 1 and 4. It goes through (0.5, 1), (1, negative 2), and (2, negative 3). Another curve opens down and to the left in quadrant 3. It goes through (negative 4, negative 4.5) and (negative 2, negative 5).

On a coordinate plane, a curve opens up and to the right in quadrants 1 and 4. It approaches the y-axis in quadrant 1, and then curves down through (0.5, negative 3) and then approaches y = negative 4. Another curves opens down and to the left in quadrant 3. It approaches y = negative 4 and then curves down through (negative 1, negative 4.5).

On a coordinate plane, a curve opens up and to the right in quadrant 1. It goes through (2, 5) and (3, 4.5). Another curve opens down and to the left in quadrants 2 and 3. It goes through (negative 1, 2) and curves down through (negative 0.5, negative 1).

On a coordinate plane, a curve opens up and to the right in quadrant 1. It goes through (1, 4.5) and (4, 4). Another curve opens down and to the left in quadrants 2 and 3. It approaches y = 4 and then curves down and approaches the y-axis in quadrant 3.

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Which type of transformation preserves the symmetry of an even function f(x) but does not preserve the symmetry of an odd function g(x)?

vertical translation

horizontal translation

reflection over the x-axis

reflection over the y-axis

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

The graph is translated left 5 units, compressed vertically by a factor of , and translated up 3 units.

The graph is stretched vertically by a factor of , translated left 5 units, and translated up 3 units.

The graph is translated left 5 units, compressed horizontally by a factor of , and translated down 3 units.

The graph is stretched horizontally by a factor of , translated left 5 units, and translated down 3 units.

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

y = StartFraction 1 Over x + 2 EndFraction + 3

y = 0.2 Superscript x Baseline + 3

y = x cubed + 3

y = log x + 3

The graph models the heights, in feet, of two objects dropped from different heights after x seconds.

g(x) = f(x) – 5

g(x) = f(x – 5)

g(x) = f(x) + 5

g(x) = f(x + 5)

A function is graphed on a coordinate grid. As the domain values approach infinity, the range values approach infinity. As the domain values approach negative infinity, the range values approach infinity. To which family of functions might the described function belong?

reciprocal

square root

exponential

quadratic

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

y = x cubed minus 4

y = (x minus 4) cubed

y = (negative x minus 4) cubed

y = (negative x) cubed minus 4

Which two transformations must be applied to the graph of y = ln(x) to result in the graph of y = –ln(x) + 64?

reflection over the x-axis, plus a vertical translation

reflection over the y-axis, plus a vertical translation

reflection over the x-axis, plus a horizontal translation

reflection over the y-axis, plus a horizontal translation

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 total sound power, in decibels, from x objects each producing 50 decibels of sound power is given by the function f(x) = 50 + 10 log x. Suppose each of the x objects increases its sound power by 10 decibels, so that the new total sound power, in decibels, is given by the function g(x) = f(x) + 10.

On a coordinate plane y = g (x) starts at (0, 60) and curves up through (10, 70). Y = f (x) starts at (0, 50) and curves up through (10, 60).

On a coordinate plane y = f (x) starts at (0, 50) and curves up through (10, 60). y = g (x) starts at (0, 40) and curves up through (10, 50).

On a coordinate plane, y = f (x) starts at (0, 50) and curves up through (10, 60). Y = g (x) starts at (10, 50) and curves up through (20, 60).

On a coordinate plane, y = g (x) starts at (negative 10, 50) and curves up through (0, 60). Y = f (x) starts at (0, 50) and curves up through (10, 60).

The graph below belongs to which function family?

linear

quadratic

cubic

absolute value

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

Review the expressions for j(x) and j(–x)j(x) =j(–x) =

j(x) is an odd function.

j(x) is an even function.

j(x) is both an even and an odd function.

j(x) is neither an even nor an odd function.

The value of a graphed function doubles for each increase of 1 in the value of x. Which of the following could be the parent function of the graphed function?

y = 2 Superscript x

y = x squared

y = StartAbsoluteValue x EndAbsoluteValue

y = StartRoot x EndRoot

The function h(x) = 12x8 + 49 is an even function. Which transformation of h(x) would result in a function that is neither even nor odd?

reflection over the x-axis

vertical stretch by a factor of 7

translation 8 units to the right

horizontal compression by a factor of

Review the graph of y = .

On a coordinate plane, a line approaches y = 6 in quadrant 2, increases through inflection point (0, 8), and then approaches y = 10 in quadrant 1.

On a coordinate plane, a line approaches y = negative 10 in quadrant 3, increases through inflection point (0, negative 8), and then approaches y = negative 6 in quadrant 4.