Question

If you apply these changes to the linear parent function, f(x) = x, what is the equation of the new function?• Vertically stretch by a factor of 7.• Shift right 9 units.

Answer 1

Explanation

The following are two rules of transformations of functions:

• a·f(x), where a > 1, stretches the curve vertically by a factor of a.

,

• f(x - r) moves the function r units right.

In this case, we have:

• Since the parent function is vertically stretched by a factor of 7 and 7 > 1, the equation for the new function is:

$\begin{gathered} a=7 \\ f(x)=x \\ \text{ Then} \\ a\cdot f(x)=7x \\ g(x)=7x \end{gathered}$

• Since the parent function shift right 9 units, the equation for the new function is:

$\begin{gathered} r=9 \\ g(x-r)=7(x-9) \\ h(x)=7(x-9) \end{gathered}$Answer

The equation of the new function is:

$h(x)=7(x-9)$