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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 absolute value function fx=|x| decreasing? - ∈ fty , ∈ fty - ∈ fty ,0 -6,0 0, ∈ fty

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    Gauthmathier8469

    Grade 12 · 2021-07-22

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

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    Gauthmathier8385

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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

    We're asked to graph:

    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

    We're asked to graph:

    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 to learn more about absolute value graphs? Check out this video.

    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

    Source : www.khanacademy.org

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