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

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## Over which interval is the graph of the parent abs

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## Over which interval is the graph of the parent absolute value function fx=|x| decreasing? - ∈ fty , ∈ fty - ∈ fty ,0 -6,0 0, ∈ fty

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

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Related Questions

Over which of the intervals below is the given absolute value function always decreasing?（   ）

$$f(x)=|x+2|$$ A. $$-4\leq x\leq -2$$ B. $$-2\leq x\leq 2$$ C. $$-2\leq x\leq 0$$ D. $$0\leq x\leq 2$$

Describe the following characteristics of the graph of the parent function $$f(x) = |x|$$: domain, range, intercepts, symmetry, continuity, end behavior, and intervals on which the graph is increasing/decreasing.

Describe the following characteristics of the graph of each parent function: domain, range, intercepts, symmetry, continuity, end behavior, and intervals on which the graph is increasing/decreasing.

$$f(x)=x$$

Describe the following characteristics of the graph of the parent function $$f\left(x\right)=x^{2}$$: domain, range, intercepts, symmetry, continuity, end behavior, and intervals on which the graph is increasing/decreasing.

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## Absolute Value Functions and Translations Flashcards

Start studying Absolute Value Functions and Translations. Learn vocabulary, terms, and more with flashcards, games, and other study tools.

## Absolute Value Functions and Translations

3.7 30 Reviews

Over which interval is the graph of the parent absolute value function f(x)= |x| decreasing?

Click card to see definition 👆

B (-∞, 0)

Click again to see term 👆

Which equation represents the function graphed on the coordinate plane?

Click card to see definition 👆

B g(x) = |x + 4| – 10

Click again to see term 👆

1/14 Created by squeaky_nugget

### Terms in this set (14)

Over which interval is the graph of the parent absolute value function f(x)= |x| decreasing?

B (-∞, 0)

Which equation represents the function graphed on the coordinate plane?

B g(x) = |x + 4| – 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?

NOT A

The graph shows the function f(x) = |x – h| + k. What is the value of k?

A k = –2.5

The graph shows the function f(x) = |x – h| + k. What is the value of h?

NOT D (h = 3.5)

The graph of is shown. On which interval is this graph increasing?

NOT C (6, ∞)

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

A

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

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?

C

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

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

C (-5, -6)

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

1. f(x) = |x|2. f(x) = |x| + 34. f(x) = |x| − 6

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

B {y | y > –2}

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

B

The graph of g(x) = |x – h| + k is shown on the coordinate grid. What must be true about the signs of h and k?

D

h must be negative and k must be positive.

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## Absolute value graph and function review (article)

The general form of an absolute value function is f(x)=a|x-h|+k. From this form, we can draw graphs. This article reviews how to draw the graphs of absolute value functions.

Graphs of absolute value functions

## Absolute value graphs review

The general form of an absolute value function is f(x)=a|x-h|+k. From this form, we can draw graphs. This article reviews how to draw the graphs of absolute value functions.

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General form of an absolute value equation:

f(x)=\goldD{a}|x-\blueD{h}|+\blueD{k}

f(x)=a∣x−h∣+k

f, left parenthesis, x, right parenthesis, equals, start color #e07d10, a, end color #e07d10, vertical bar, x, minus, start color #11accd, h, end color #11accd, vertical bar, plus, start color #11accd, k, end color #11accd

The variable \goldD{a} a

start color #e07d10, a, end color #e07d10

tells us how far the graph stretches vertically, and whether the graph opens up or down. The variables

\blueD h h

start color #11accd, h, end color #11accd

and \blueD k k

start color #11accd, k, end color #11accd

tell us how far the graph shifts horizontally and vertically.

Some examples: \small{2} 2 \small{4} 4 \small{\llap{-}4} - 4 \small{2} 2 \small{4} 4 \small{\llap{-}4} - 4 y y x x

A coordinate plane. The x- and y-axes both scale by one. The graph is of the function y equals the absolute value of x. The vertex is at the point zero, zero. The points negative one, one and one, one can be found on the graph.

Graph of y=|x| \small{2} 2 \small{4} 4 \small{\llap{-}4} - 4 \small{2} 2 \small{4} 4 \small{\llap{-}4} - 4 y y x x Graph of y=3|x| \small{2} 2 \small{4} 4 \small{\llap{-}4} - 4 \small{2} 2 \small{4} 4 \small{\llap{-}4} - 4 y y x x Graph of y=-|x| \small{2} 2 \small{4} 4 \small{\llap{-}4} - 4 \small{2} 2 \small{4} 4 \small{\llap{-}4} - 4 y y x x Graph of y=|x+3|-2

### Example problem 1

f(x)=|x-1|+5 f(x)=∣x−1∣+5

f, left parenthesis, x, right parenthesis, equals, vertical bar, x, minus, 1, vertical bar, plus, 5

First, let's compare with the general form:

f(x)=\goldD{a}|x-\blueD{h}|+\blueD{k}

f(x)=a∣x−h∣+k

f, left parenthesis, x, right parenthesis, equals, start color #e07d10, a, end color #e07d10, vertical bar, x, minus, start color #11accd, h, end color #11accd, vertical bar, plus, start color #11accd, k, end color #11accd

The value of \goldD a a

start color #e07d10, a, end color #e07d10

is 1 1 1

, so the graph opens upwards with a slope of

1 1 1

(to the right of the vertex).

The value of \blueD h h

start color #11accd, h, end color #11accd

is 1 1 1 and the value of \blueD k k

start color #11accd, k, end color #11accd

is 5 5 5

, so the vertex of the graph is shifted

1 1 1 to the right and 5 5 5 up from the origin.

Finally here's the graph of

y=f(x) y=f(x)

y, equals, f, left parenthesis, x, right parenthesis

: \small{2} 2 \small{4} 4 \small{6} 6 \small{8} 8 \small{2} 2 \small{4} 4 \small{6} 6 \small{8} 8 y y x x

### Example problem 2

f(x)=-2|x|+4 f(x)=−2∣x∣+4

f, left parenthesis, x, right parenthesis, equals, minus, 2, vertical bar, x, vertical bar, plus, 4

First, let's compare with the general form:

f(x)=\goldD{a}|x-\blueD{h}|+\blueD{k}

f(x)=a∣x−h∣+k

f, left parenthesis, x, right parenthesis, equals, start color #e07d10, a, end color #e07d10, vertical bar, x, minus, start color #11accd, h, end color #11accd, vertical bar, plus, start color #11accd, k, end color #11accd

The value of \goldD a a

start color #e07d10, a, end color #e07d10

is -2 −2 minus, 2

, so the graph opens downwards with a slope of

-2 −2 minus, 2

(to the right of the vertex).

The value of \blueD h h

start color #11accd, h, end color #11accd

is 0 0 0 and the value of \blueD k k

start color #11accd, k, end color #11accd

is 4 4 4

, so the vertex of the graph is shifted

4 4 4 up from the origin.

Finally here's the graph of

y=f(x) y=f(x)

y, equals, f, left parenthesis, x, right parenthesis

: \small{2} 2 \small{4} 4 \small{\llap{-}4} - 4 \small{2} 2 \small{4} 4 \small{\llap{-}4} - 4 y y x x

Want more practice? Check out this exercise.

## Graphs of absolute value functions

Shifting absolute value graphs

Practice: Shift absolute value graphs

Scaling & reflecting absolute value functions: equation