Functions and Transformations Answers
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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 rightB
horizontal stretch by a factor of 4, and a translation 27 units downC
horizontal compression by a factor of , and a translation 27 units right
D
horizontal compression by a factor of , and a translation 27 units down2
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Review the graph of f(x) = and the graph of the transformed function g(x).
A
–2f(x + 4)B
–2f(x – 4)C
–f(x + 4)D
–f(x – 4)3
Review the expressions for j(x) and j(–x)j(x) =j(–x) =
A
j(x) is an odd function.B
j(x) is an even function.C
j(x) is both an even and an odd function.D
j(x) is neither an even nor an odd function.4
Consider the function f(x) = x5 – 3x2 + 5x. Let g(x) = f(–x + 4).Which shows the graphs of f(x) and g(x)?
A
On a coordinate plane, y = f (x) goes through (negative 0.5, negative 3) and (0, 0) to an inflection point around (0.8, 2.6) and then curves up through (1, 3). Y = g (x) goes through (4.5, negative 3) through (4, 0) to an inflection point around (3.3, 2.4) and then curves up through (3, 3).
B
On a coordinate plane, y = f (x) goes through (negative 0.5, negative 3) and (0, 0) to an inflection point around (0.8, 2.6), and then curves up through (1, 3). Y = g (X) goes through (negative 3.5, negative 3) and (negative 4, 0) to an inflection point around (negative 4.5, 2.4) and curves up through (negative 5, 3).
C
On a coordinate plane, y = f (x) goes through (negative 0.5, negative 3) and (0, 0) to an inflection point around (0.8, 2.6), and then curves up through (1, 3). Y = g (x) goes through (5, negative 3) to an inflection point around (4.5, negative 2.5) and curves up through 4, 0).
D
On a coordinate plane, y = f (x) goes through (negative 0.5, negative 3) and (0, 0) to an inflection point around (0.8, 2.6), and then curves up through (1, 3). Y = g (x) goes through (negative 3, negative 3) to an inflection point around (negative 3.2, negative 2.5) and curves up through (negative 4, 0).
5
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.
A
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).
B
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).
C
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).
D
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).
6
Which is the graph of ?
A
On a coordinate plane, a curve starts at (0, 2) and curves up through (30, 5) and (70, 6).
B
On a coordinate plane, a curve starts at (0, 0) and curves up through (50, 3) and (80, 3.5).
C
On a coordinate plane, a curve starts at (0, 0) and curves up through (60, 5) and (80, 5.5).
D
On a coordinate plane, a curve starts at (0, 0) and curves up through (60, 8) and (70, 8.4).
7
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).
B
On a coordinate plane, a curve approaches the y-axis in quadrant 4 and increases up through (1, 0.5) and (5, 2).
C
On a coordinate plane, a curve approaches x = negative 3 and curves up through (negative 2, 0) and goes through (1, 1).
D
On a coordinate plane, a curve approaches x = 3 and curves up through (4, 0).
8
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).
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).
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).
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).
9
Review the graphs of f(x) = –x5 + 2x4 + 1 and g(x), which is a translation of f(x).
A
g(x) = (–x5 + 2x4 + 1) + 2B
g(x) = –(x + 2)5 + 2(x + 2)4 + 1C
g(x) = (–x5 + 2x4 + 1) – 2D
g(x) = –(x – 2)5 + 2(x – 2)4 + 110
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-axisB
vertical stretch by a factor of 7C
translation 8 units to the rightD
horizontal compression by a factor of
11
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.
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.12
Which describes changes to the graph of w(x), when applying the transformation w(x – 19)?
A
A point (r, s) on the graph of w(x) moves to (r – 19, s).B
A point (r, s) on the graph of w(x) moves to (r, s – 19).C
A point (r, s) on the graph of w(x) moves to (r + 19, s).D
A point (r, s) on the graph of w(x) moves to (r, s + 19).13
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).
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).
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).
D
On a coordinate plane, a line approaches the x-axis in quadrant 2 and then curves up through (0, 1) and (1, 3).
14
The graph models the projected populations, in thousands, of two towns after x years. Both towns experience a 1.9% annual growth rate.
A
g(x) = f
B
g(x) = f
C
g(x) = f(x) +
D
g (x) = five-thirds times f (x)
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