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Functions and Transformations Answers

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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).
Option A
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).
Option B
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).
Option C
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).
Option D
2
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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
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-axis
B
vertical stretch by a factor of 7
C
translation 8 units to the right
D
horizontal compression by a factor of
4

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
5

Consider the function m(x) = 2x.Which is the graph of m(x)?

Question illustration
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.
Option A
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.
Option B
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.
Option C
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.
Option D
6

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).
Option A
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).
Option B
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).
Option C
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).
Option D
7

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).
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).
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
9

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)
10

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

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