Absolute Value Functions and Translations Answers

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Which functions have a vertex with a x-value of 0? Select three options.f(x) = |x|f(x) = |x| + 3f(x) = |x + 3|f(x) = |x| − 6f(x) = |x + 3| – 6

A
f(x) = |x|
B
f(x) = |x| + 3
C
f(x) = |x + 3|
D
f(x) = |x| − 6
E
f(x) = |x + 3| – 6
2
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Which graph represents the function h(x) = |x| + 0.5?

A
Option
B
Option
C
Option
D
Option
3

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)
4

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

A
Option
B
Option
C
Option
D
Option
5

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)
6

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}
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 + 2| as a solid line?

A
Option
B
Option
C
Option
D
Option
8

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

Question illustration
A
(–∞, ∞)
B
(–∞, 0)
C
(–6, 0)
D
(0, ∞)
9

On a coordinate plane, an absolute value graph has a vertex at (1, negative 2.5).

Question illustration
A
k = –2.5
B
k = –1
C
k = 1
D
k = 2.5
10

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.

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