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Functions and Transformations Answers

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The graph models the projected populations, in thousands, of two towns after x years. Both towns experience a 1.9% annual growth rate.

Question illustration
A
g(x) = f
Option A
B
g(x) = f
Option B
C
g(x) = f(x) +
Option C
D
g (x) = five-thirds times f (x)
Option D
2
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Which is the graph of y = log4(x+3)?

A
On a coordinate plane, a curve starts at (0, 0) and curves up through (1, 3) and goes through (4, 4).
Option A
B
On a coordinate plane, a curve approaches the y-axis in quadrant 4 and increases up through (1, 0.5) and (5, 2).
Option B
C
On a coordinate plane, a curve approaches x = negative 3 and curves up through (negative 2, 0) and goes through (1, 1).
Option C
D
On a coordinate plane, a curve approaches x = 3 and curves up through (4, 0).
Option D
3

Which transformations to the graph of j(x) would result in the graph of j(4x) – 27?

A
horizontal stretch by a factor of 4, and a translation 27 units right
B
horizontal stretch by a factor of 4, and a translation 27 units down
C
horizontal compression by a factor of , and a translation 27 units right
Option C
D
horizontal compression by a factor of , and a translation 27 units down
Option D
4

Which graph represents an odd function?

A
On a coordinate plane, a line curves down from quadrant 2 through (negative 2, 0) to (negative 1.5, negative 6). It then curves up through (negative 1, negative 5) through (0, 0) to (0.5, 0.4). It then curves down to (1, 0) and then curves up through (1.5, 2).
Option A
B
On a coordinate plane, a line curves up from quadrant 3 through (negative 2, 0) to (negative 1.6, 1.3). It then curves down through (0, 0) to (1.4, negative 1.3) and curves up through (2, 0).
Option B
C
On a coordinate plane, a line curves down from quadrant 2 through (negative 2, 0) to (negative 1.7, negative 1.8). It then curves up through (negative 1, 2) to (0, 5). It then curves down through (2, 1) to (1.8, negative 1.8). It then curves up through (2, 0).
Option C
D
On a coordinate plane, a line approaches the x-axis in quadrant 2 and then curves up through (0, 1) and (1, 3).
Option D
5

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?

A
reflection over the x-axis
B
vertical stretch by a factor of 7
C
translation 8 units to the right
D
horizontal compression by a factor of
Option D
6

Review the graph of f(x) = and the graph of the transformed function g(x).

Question illustration
A
–2f(x + 4)
B
–2f(x – 4)
C
–f(x + 4)
D
–f(x – 4)
7

Which is the graph of ?

Question illustration
A
On a coordinate plane, a curve starts at (0, 2) and curves up through (30, 5) and (70, 6).
Option A
B
On a coordinate plane, a curve starts at (0, 0) and curves up through (50, 3) and (80, 3.5).
Option B
C
On a coordinate plane, a curve starts at (0, 0) and curves up through (60, 5) and (80, 5.5).
Option C
D
On a coordinate plane, a curve starts at (0, 0) and curves up through (60, 8) and (70, 8.4).
Option D
8

Review the graphs of f(x) = –x5 + 2x4 + 1 and g(x), which is a translation of f(x).

Question illustration
A
g(x) = (–x5 + 2x4 + 1) + 2
B
g(x) = –(x + 2)5 + 2(x + 2)4 + 1
C
g(x) = (–x5 + 2x4 + 1) – 2
D
g(x) = –(x – 2)5 + 2(x – 2)4 + 1
9

Consider the function f(x) = x3 + 0.5x – 1. Marjan needs to graph f(x) and g(x) = –f(x) – 3. His graphs are shown below.

Question illustration
A
No, the reflection should be over the x-axis, not the y-axis.
B
No, the reflection should be over the y-axis, not the x-axis.
C
Yes, g(x) is a reflection of f(x) over the y-axis followed by a translation of 3 units down.
D
Yes, g(x) is a reflection of f(x) over the x-axis followed by a translation of 3 units down.
10

Which is the graph of y = (x – 1)4 – 3?

A
On a coordinate plane, a parabola opens up. It goes through (negative 0.5, 0), has a vertex at (1, negative 3), and goes through (2, negative 2).
Option A
B
On a coordinate plane, a parabola opens up. It goes through (negative 2, negative 2), has a vertex at (negative 1, negative 3), and goes through (0, negative 2).
Option B
C
On a coordinate plane, a parabola opens up. It goes through (2, 0), has a vertex at (3, negative 1), and goes through (4, 0).
Option C
D
On a coordinate plane, a parabola opens up. It goes through (negative 4, 0), has a vertex at (negative 3, negative 1), and goes through (negative 2, 0).
Option D

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