Question

describe a function that transforms the parent root function with a horizontal compression by a factor of 3 and a downward shift of 15 units.

Answer 1

Answer:

g(x) = f(3x) -15

Step-by-step explanation:

Let f(x) be the parent function.

If the function is to be compressed by a factor of 3 horizontally, we must obtain the value f(3) when x=1, for example. We can do that by using 3x as the argument of the function:

  g(x) = f(3x)

If its graph is to be shifted downward by 15 units, every value produced by the function must have -15 added to it. That is, the shifted function is ...

  g(x) = f(3x) - 15

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The attached graph shows an example function compressed horizontally and vertically shifted.