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?

Option

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

(–6, –5)

(–6, 5)

(–5, –6)

(5, –6)

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

(–∞, ∞)

(–∞, 0)

(–6, 0)

(0, ∞)

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

(6, 8)

(8, 6)

(6, –8)

(–8, 6)

Which functions have a vertex with a x-value of 0? Select three options.

f(x) = |x|

f(x) = |x| + 3

f(x) = |x + 3|

f(x) = |x| − 6

f(x) = |x + 3| – 6

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

k = –2.5

k = –1

k = 1

k = 2.5

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

On a coordinate plane, an absolute value graph has a vertex at (0, 3).

On a coordinate plane, an absolute value graph has a vertex at (negative 3, 0).

On a coordinate plane, an absolute value graph has a vertex at (0, negative 3).

On a coordinate plane, an absolute value graph has a vertex at (3, 0).

On a coordinate plane, an absolute value graph has a vertex at (negative 1.5, negative 3.5).

h = –3.5

h = –1.5

h = 1.5

h = 3.5

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

Both h and k must be positive.

Both h and k must be negative.

h must be positive and k must be negative.

h must be negative and k must be positive.

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

{y | y > –2}

{y | y > 12}

Absolute Value Functions and Translations Answers

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