Question

Define a function that transforms the parent root function with a horizontal compression by a factor of 2 and a downward shift of 6 unit

Answer 1

The horizontal compression by a factor of 2 of a function f(x) is expressed as:

$f(x)\to2f(x)$

Now, for a downward shift of 6 units:

$f(x)\to f(x)-6$

If the parent function is:

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

Now, combining the transformations above:

$\begin{gathered} f(x)\to2f(x)-6 \\ \Rightarrow f(x)=2\sqrt[n]{x}-6 \end{gathered}$