Functions and Transformations Answers
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1
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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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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)
3
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 of4
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).
5
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).
6
Review the graph of y = .
A
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.
B
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.
C
On a coordinate plane, a line approaches y = 10 in quadrant 2, decreases through inflection point (0, 8), and then approaches y = 6 in quadrant 1.
D
Option
7
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).
8
Consider the function m(x) = 2x.Which is the graph of m(x)?
A
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then curves up through (0, 3) and (1, 6) into quadrant 1.
B
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then curves up through (0, 0.6) and (4, 5) into quadrant 1.
C
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then curves up through (0, 1) and (1, 7) into quadrant 1.
D
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then curves up through (0, 1) and (3, 2) into quadrant 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.
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
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).
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