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
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