Absolute Value Functions and Translations Answers

1

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

A

h = –3.5

B

h = –1.5

C

h = 1.5

D

h = 3.5

1

Free Preview

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

A

g(x) = |x – 4| – 10

B

g(x) = |x + 4| – 10

C

g(x) = |x – 10| + 4

D

g(x) = |x + 10| – 4

2

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).

2

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)

2

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

A

(–∞, ∞)

B

(–∞, 0)

C

(–6, 0)

D

(0, ∞)

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

3

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

A

Option

B

Option

C

Option

D

Option

4

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

A

Option

B

Option

C

Option

D

Option

4

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

A

h = –3.5

B

h = –1.5

C

h = 1.5

D

h = 3.5

5

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

A

(–∞, ∞)

B

(–∞, 0)

C

(–6, 0)

D

(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 + 2| as a solid line?

A

Option

B

Option

C

Option

D

Option

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

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}

6

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.

6

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)

7

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 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

7

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.

8

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)

8

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

A

Option

B

Option

C

Option

D

Option

8

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}.

8

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}

9

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

A

(–∞, 6)

B

(–∞, 10)

C

(6, ∞)

D

(10, ∞)

9

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

9

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

A

(–∞, 6)

B

(–∞, 10)

C

(6, ∞)

D

(10, ∞)

10

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}.

10

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

A

g(x) = |x – 4| – 10

B

g(x) = |x + 4| – 10

C

g(x) = |x – 10| + 4

D

g(x) = |x + 10| – 4

10

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).

10

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

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