Absolute Value Functions Answers

1

Free Preview

Find the vertex of the given function. f(x) = |x – 5| + 10 The vertex is at ([___], [___]).

Answer:

5

1

Free Preview

What are the domain and range of the function?

A

Option

B

Option

C

Option

D

Option

1

Question text not available

Answers:

Blank 1:-1

Blank 2:-7

1

Find the vertex of the given function. f(x) = |x + 1| - 7 The vertex is at ([___], [___]).

Answer:

(-1, -7)

1

Which of the following is a horizontal stretch of the parent function?

A

Option

B

Option

C

Option

1

Which graph shows f(x) = 0.5|x + 3| – 2?

A

Option

B

Option

C

Option

1

Which graph shows f(x) = |x| reflected across the x-axis, translated 2 units down and 1 unit to the left?

A

Option

B

Option

C

Option

1

Given the function f(x) = 4|x – 5| + 3, for what values of x is f(x) = 15?

A

x = 2, x = 8

B

x = 1.5, x = 8

C

x = 2, x = 7.5

D

x = 0.5, x = 7.5

1

The standard diameter of a golf ball is 42.67 mm.A golf ball factory does quality control on the golf balls it manufactures. Golf balls are randomly measured to ensure the correct size. If the discrepancy in diameter is more than 0.004 mm, the production is stopped.Which function could represent this situation?f(x) = |x – 42.67|f(x) = |42.67 – x|f(x) = |42.67 + x|

A

f(x) = |x – 42.67|

B

f(x) = |42.67 – x|

C

f(x) = |42.67 + x|

1

The graph of an absolute value function has a vertex at (–2, 3) and passes through the point (–1, 0). Using transformations of the parent function, has the graph been dilated by a scale factor other than 1? Explain.

Answer:

Yes. The equation is y = -3|x + 2| + 3, so the graph has a dilation with scale factor 3, along with a reflection across the x-axis.

1

Find the vertex of the given function. f(x) = |x – 5| + 10 The vertex is at (, ).

Answer:

5

1

Find the vertex of the given function. f(x) = |x + 1| - 7 The vertex is at (, ).

Answer:

-1

1

Which of the following is a horizontal stretch of the parent function?

A

Option

B

Option

C

Option

1

Which graph shows f(x) = 0.5|x + 3| – 2?

A

Option

B

Option

C

Option

1

Which graph shows f(x) = |x| reflected across the x-axis, translated 2 units down and 1 unit to the left?

A

mc001-1.jpg

B

mc001-2.jpg

C

mc001-3.jpg

1

Given the function f(x) = 4|x – 5| + 3, for what values of x is f(x) = 15?

Answer not available

1

What are the acceptable diameters for the golf balls?

A

42.675 mm

B

42.6668 mm

C

42.664 mm

D

42.673 mm

E

72.676 mm

1

The graph of an absolute value function has a vertex at (–2, 3) and passes through the point (–1, 0). Using transformations of the parent function, has the graph been dilated by a scale factor other than 1? Explain.

Answer:

Yes, the graph has been dilated by a scale factor of 3. To determine this, use the standard form of an absolute value function, y = a|x – h| + k, where (h, k) is the vertex. Substituting the vertex (-2, 3) and the point (-1, 0) into the equation gives 0 = a|(-1) – (-2)| + 3. Simplifying this results in 0 = a(1) + 3, which means a = –3. Since the absolute value of a is 3 (not 1), the graph has undergone a vertical stretch (dilation).

2

Find the vertex of the given function. f(x) = |x + 1| - 7 The vertex is at ([___], [___]).

Answer:

(-1, -7)

2

Which equation represents the reflected and translated function? f(x) = –|x – 2| – 1f(x) = –|x + 1| – 2 f(x) = |x + 2| – 1

A

f(x) = –|x – 2| – 1

B

f(x) = –|x + 1| – 2

C

f(x) = |x + 2| – 1

2

Given the function f(x) = –0.5|2x + 2| + 1, for what values of x is f(x) = 6?

A

x = 6, x = –5

B

x = 5, x = –5

C

x = 7, x = –6

D

no solution

2

What are the acceptable diameters for the golf balls?

A

42.675 mm

B

42.6668 mm

C

42.664 mm

D

42.673 mm

E

72.676 mm

2

Which of the following did you include in your answer?

A

Yes, the graph has been dilated.

B

Using the standard form of the equation, substitute in the values: h = –2, k = 3, x = –1, and y = 0.

C

Solve the equation to get a = –3.

D

Graphically, the parent function follows the pattern of right 1, up 1. Moving 1 unit to the right from the vertex, you can move down 3 units to get to the point (–1, 0), so it has been horizontally compressed.

2

Question text not available

Answer:

10

2

Question text not available

Answer:

-7

2

Which equation represents the reflected and translated function?

A

f(x) = –|x – 2| – 1

B

f(x) = –|x + 1| – 2

C

f(x) = |x + 2| – 1

2

Given the function f(x) = –0.5|2x + 2| + 1, for what values of x is f(x) = 6?

Answer not available

2

Select question c94b957d

A

f(x) = |x – 42.67|

B

f(x) = |42.67 – x|

C

f(x) = |42.67 + x|

2

Which of the following did you include in your answer?

A

Yes, the graph has been dilated.

B

Using the standard form of the equation, substitute in the values: h = –2, k = 3, x = –1, and y = 0.

C

Solve the equation to get a = –3.

D

Graphically, the parent function follows the pattern of right 1, up 1. Moving 1 unit to the right from the vertex, you can move down 3 units to get to the point (–1, 0), so it has been horizontally compressed.

3

What are the domain and range of the function?

A

Option

B

Option

C

Option

D

Option

3

What are the domain and range of the function?