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<k<1`, 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`.