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

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

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

_____

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

Answer 2

`f(x)=\sqrt[n]{3x} -15`

Explanation:

Parent root function:

`f(x)=\sqrt[n]{x}`

According to rules,

• Compression would be achieved by multiplying the
  `x` by 3. So, we would have
  `f(x)=\sqrt[n]{3x}`.
• Downward vertical shift would be achieved by adding a
  `-10` to the function. So,
  `\sqrt[n]{3x} -15`.

Answer:

`f(x)=\sqrt[n]{3x} -15`