Question

If f(x)=x^2 is vertically stretched by a factor of 9 to g(x). What is the equation of g(x)?

Answer 1

Given:

The function is:

$f(x)=x^2$

This function is stretched by a factor of 9 to g(x).

To find:

The equation of function function g(x).

Solution:

The vertical stretch is defined as:

$g(x)=kf(x)$           ...(i)

If $0$, then the function f(x) compressed vertically by factor k.

If $k>1$, then the function f(x) stretched vertically by factor k.

The given function f(x) is stretched by a factor of 9 to g(x).  So the value of k is 9.

Substituting $k=9$ in (i), we get

$g(x)=9f(x)$

$g(x)=9x^2$            $[\because f(x)=x^2]$

Therefore, the required function is $g(x)=9x^2$.