Answer:
Horizontal stretch by a factor of 3
Step-by-step explanation:
Given:
[tex]f(x)=\cos\frac{x}{3}[/tex]
[tex]g(x)=\cos x[/tex]
Function transformation rule used:
[tex]g(x)\rightarrow f(x\times C})[/tex]
When [tex]x[/tex] is multiplied by a constant [tex]C[/tex] then the function is either stretched or compressed in horizontal direction.
If the [tex]C>1[/tex] then its a horizontal compress.
If the [tex]C<1[/tex] then its a horizontal stretch.
Function transformation taking place:
[tex]g(x)\rightarrow f(\frac{x}{3})[/tex]
The constant term multiplied in the above transformation comes to be [tex]\frac{1}{3}[/tex] which is [tex]<1[/tex], which means that the transformation would be a horizontal stretch by a factor of 3.
