which function g represents the exponential function f(x)=3^x after a horizontal stretch by a factor of 4 and a reflection across the y-axis

Question

which function g represents the exponential function f(x)=3^x after a horizontal stretch by a factor of 4 and a reflection across the y-axis?

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Gia Bảo 5 years 2021-08-28T15:54:07+00:00 1 Answers 16 views 0

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  1. thienan
    0
    2021-08-28T15:55:09+00:00
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    Answer: h(x) = 3^(-x/4)

    Step-by-step explanation:

    If we have a function f(x), an horizontal stretch of scale factor k is written as:

    g(x) = f(x/k)

    So, if we have the function f(x) = 3^x

    A horizontal stretch of scale factor 4 is:

    g(x) = f(x/4) = 3^(x/4)

    Now we have a reflection across the y-axis

    If we have a function f(x), a reflection across the x-axis is written as:

    g(x) = f(-x)

    Then if now we apply a reflection across the y-axis to the function g(x), we have:

    h(x) = g(-x) = 3^(-x/4)

    Then the transformation that we wanted is:

    h(x) = 3^(-x/4)

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