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I'm trying to describe how the graph is related to the parent function.

The parent function is x^3

and the problem is:


I know its a reflection over the x-axis, but what is the formula for how much it expands or shrinks?

Like on another problem it's


and y= |0.2x|

The answer is that it expands by 5, but I'm not exactly sure how to get it.


  • pre-calculus -

    -(0.8x)^3 is stretching in the x-axis by a factor of (1/0.8) and as you noted, a reflection about the x-axis.

    When ever the function f(x) is mapped to another by f(kx), it is stretching or contracting by a factor of (1/k). (1/k)>1 is a stretching, and (1/k)<1 is contracting.

  • pre-calculus -more -

    The stretching factor (1/k) applies to the x-direction only.

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