Absolute Value Functions and Translations Answers

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What is the range of the function g(x) = |x – 12| – 2?

A
{y | y > –2}
B
{y | y > –2}
C
{y | y > 12}
D
{y | y > 12}
4

Over which interval is the graph of the parent absolute value function decreasing?

Question illustration
A
(–∞, ∞)
B
(–∞, 0)
C
(–6, 0)
D
(0, ∞)
5

On a coordinate plane, an absolute value graph has a vertex at (negative 2, 1).

Question illustration
A
Both h and k must be positive.
B
Both h and k must be negative.
C
h must be positive and k must be negative.
D
h must be negative and k must be positive.
6

What is the vertex of the graph of f(x) = |x + 5| – 6?

A
(–6, –5)
B
(–6, 5)
C
(–5, –6)
D
(5, –6)
7

On each coordinate plane, the parent function f(x) = |x| is represented by a dashed line and a translation is represented by a solid line. Which graph represents the translation g(x) = |x| – 4 as a solid line?

Question illustration
A
Option
B
Option
C
Option
D
Option
8

Which graph represents the function r(x) = |x – 2| – 1

Question illustration
A
Option
B
Option
C
Option
D
Option
9

Which graph represents the function f(x) = |x + 3|?

A
On a coordinate plane, an absolute value graph has a vertex at (0, 3).
Option A
B
On a coordinate plane, an absolute value graph has a vertex at (negative 3, 0).
Option B
C
On a coordinate plane, an absolute value graph has a vertex at (0, negative 3).
Option C
D
On a coordinate plane, an absolute value graph has a vertex at (3, 0).
Option D
10

What is the vertex of the graph of g(x) = |x – 8| + 6?

A
(6, 8)
B
(8, 6)
C
(6, –8)
D
(–8, 6)
20

On each coordinate plane, the parent function f(x) = |x| is represented by a dashed line and a translation is represented by a solid line. Which graph represents the translation g(x) = |x + 2| as a solid line?

Question illustration
A
Option
B
Option
C
Option
D
Option
21

What is the vertex of the graph of f(x) = |x + 5| – 6?

A
(–6, –5)
B
(–6, 5)
C
(–5, –6)
D
(5, –6)
22

On a coordinate plane, an absolute value graph has a vertex at (10, 6).

Question illustration
A
(–∞, 6)
B
(–∞, 10)
C
(6, ∞)
D
(10, ∞)
23

Which graph represents the function h(x) = |x| + 0.5?

A
Option
B
Option
C
Option
D
Option
24

On a coordinate plane, an absolute value graph has a vertex at (negative 4, negative 10).

Question illustration
A
g(x) = |x – 4| – 10
B
g(x) = |x + 4| – 10
C
g(x) = |x – 10| + 4
D
g(x) = |x + 10| – 4
26

On a coordinate plane, an absolute value graph has a vertex at (negative 4, negative 10).

Question illustration
A
g(x) = |x – 4| – 10
B
g(x) = |x + 4| – 10
C
g(x) = |x – 10| + 4
D
g(x) = |x + 10| – 4
27

What is the range of the function g(x) = |x – 12| – 2?

A
{y | y > –2}
B
{y | y > –2}
C
{y | y > 12}
D
{y | y > 12}

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