The function f(x) = 4x.  The graph of g(x) is f(x) vertically stretched by a factor of 6 and reflected in the y-axis.  What is the function rule for g(x)?

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Multiplying f(x) by 6 creates a vertical stretch of factor 6. To reflect across the y-axis we replace x with (-x).

Thus g(x)=6(4(-x))=24(-x)=-24x.


The graph of f(x) (red), 6f(x) in blue(vertical stretch) and g(x) (reflection over y-axis) (green):

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