Question

Please help! The graph of g(x) shown below is the graph of f(x)=x2 horizontally stretched by a factor of 3 write the equation for g(x)

Answer 1

The equation of g(x) is :

`g(x)=(x^2)/(9)`

EXPLANATION :

Note that stretching a function horizontally by a factor of c :

`f(x)\rightarrow f((x)/(c))`

From the problem, we have a function f(x) = x^2

and g(x) is the graph of f(x) when horizontally stretched by a factor of 3.

Then :

`g(x)=f((x)/(3))`

Substitute x/3 to the parent function f(x) = x^2 :

`\begin{gathered} g(x)=((x)/(3))^2 \\ g(x)=(x^2)/(9) \end{gathered}`