Let g(x) be the indicated transformation of f(x) = |4x| − 5. Compress the graph of f(x) = |4x| − 5 horizontally by a factor of 1/2 and reflect it across the x-axis. Identify the rule and graph of g(x).

  g(x) = -|8x| +5

Step-by-step explanation:

We assume that "compress ... by a factor of 1/2" means that horizontal distances on the graph of f(x) are to be reduced to 1/2 their value to obtain the graph of g(x). (We prefer to call this "scaled by 1/2", so that we avoid the ambiguity associated with using a fractional value as a compression factor.)

If k is the horizontal scale factor, then the horizontal scaling makes ...

  g(x) = f(x/k)

Reflection across the x-axis changes the sign of function values, so our compressed, reflected function is ...

  g(x) = -f(x/(1/2)) = -f(2x)

  g(x) = -(|4(2x)| -5)

  g(x) = -|8x| +5

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step-by-step explanation: