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25 September, 10:27

If you horizontally stretch the quadratic parent function f (x) = x^2 by a factor of 4 what's the equation of the new function

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  1. 25 September, 11:43
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    g (x) = ¹/₁₆x²

    Step-by-step explanation:

    The parent function is ƒ (x) = x².

    Then g (x) = (ax) ² is either a compression or a stretch of the parent function.

    0 < |a| < 1 is a stretch by a factor of 1/a.

    Thus, if you want to stretch a parabola by a factor of 4,

    a = ¼

    and the equation of the new function is

    g (x) = (¼x) ² or

    g (x) = ¹/₁₆x²

    The diagram below shows that

    ƒ (x) = 1 when x = 1 but

    g (x) = 1 when x = 4

    The parabola has been stretched by a factor of 4.
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