Given:
The function is:
[tex]f(x)=x^2[/tex]
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:
[tex]g(x)=kf(x)[/tex] ...(i)
If [tex]0<k<1[/tex], then the function f(x) compressed vertically by factor k.
If [tex]k>1[/tex], 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 [tex]k=9[/tex] in (i), we get
[tex]g(x)=9f(x)[/tex]
[tex]g(x)=9x^2[/tex] [tex][\because f(x)=x^2][/tex]
Therefore, the required function is [tex]g(x)=9x^2[/tex].
