Write a function g whose graph represents a horizontal stretch by a factor of 4 followed by a reflection in the y-axis of the graph of f(x)=|x|.


  1. Using translation concepts, the function g(x) is given by:
    g(x) = |x/4|

    What is a translation?

    A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
    For this problem, the parent function is given by:
    f(x) = |x|
    The changes are as follows:
    • Horizontal stretch by a factor of 4, hence x -> x/4.
    • Reflection over the y-axis, hence x -> -x. Since |x| = |-x|, this effectively does nothing for the function.
    Hence the function g(x) is given by:
    g(x) = |x/4|
    More can be learned about translation concepts at


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