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18 June, 13:33

If you shift the quartic parent function, F (x) down 7 units and reflect it across the y-axis, what is equation of the new function?

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  1. 18 June, 14:44
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    The new function g (x) will be ⇒ g (x) = f (-x) ² - 7

    Step-by-step explanation:

    * Lets take about the transformation

    - If the function f (x) reflected across the x-axis, then the new

    function g (x) = - f (x)

    - If the function f (x) reflected across the y-axis, then the new

    function g (x) = f (-x)

    - If the function f (x) translated horizontally to the right

    by h units, then the new function g (x) = f (x - h)

    - If the function f (x) translated horizontally to the left

    by h units, then the new function g (x) = f (x + h)

    - If the function f (x) translated vertically up

    by k units, then the new function g (x) = f (x) + k

    - If the function f (x) translated vertically down

    by k units, then the new function g (x) = f (x) - k

    * In the problem

    - You will shift f (x) 7 units down and reflect it across the y-axis

    - That means we will subtract f (x) by 7 and change x to - x

    * The new function g (x) will be

    g (x) = f (-x) - 7

    * Look to the graph

    - The red graph is f (x) = x²

    - The blue graph is g (x) = (-x) ² - 7
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