Functions and Transformations Answers
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1
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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.
2
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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
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).
4
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.5
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).
6
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 + 17
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).
8
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)9
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
10
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
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