Absolute Value Functions and Translations…

The graph of f(x) = |x| is translated 6 units to the right and 2 units up to form a new function. Which statement about the range of both functions is true?

A

The range is the same for both functions: {y | y is a real number}.

B

The range is the same for both functions: {y | y > 0}.

C

The range changes from {y | y > 0} to {y | y > 2}.

D

The range changes from {y | y > 0} to {y | y > 6}.

2

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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)

3

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

A

k = –2.5

B

k = –1

C

k = 1

D

k = 2.5

4

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

A

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

B

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

C

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

D

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

5

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?

A

Option

B

Option

C

Option

D

Option

6

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

A

Option

B

Option

C

Option

D

Option

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

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

A

Option

B

Option

C

Option

D

Option

9

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)

10

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

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.

11

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

B

Both h and k must be positive.

B

Both h and k must be negative.

h

h must be positive and k must be negative.

h

h must be negative and k must be positive.

12

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?

A

Option

B

Option

C

Option

D

Option

13

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

k

k = –2.5

k

k = –1

k

k = 1

k

k = 2.5

14

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

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

15

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

A

Option

B

Option

C

Option

D

Option

16

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

(

(–∞, 6)

(

(–∞, 10)

(

(6, ∞)

(

(10, ∞)

17

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

A

Option

B

Option

C

Option

D

Option

18

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

A

Option

B

Option

C

Option

D

Option

19

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

(

(–∞, ∞)

(

(–∞, 0)

(

(–6, 0)

(

(0, ∞)

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?

A

Option

B

Option

C

Option

D

Option

Absolute Value Functions and Translations Answers

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