Question

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x).

(x) = cos x divided by three; g(x) = cos x

Answer 1

Horizontal stretch by a factor of 3

Explanation:

Given:

`f(x)=\cos(x)/(3)`

`g(x)=\cos x`

Function transformation rule used:

`g(x)\rightarrow f(x* C})`

When
`x` is multiplied by a constant
`C` then the function is either stretched or compressed in horizontal direction.

If the
`C>1` then its a horizontal compress.

If the
`C<1` then its a horizontal stretch.

Function transformation taking place:

`g(x)\rightarrow f((x)/(3))`

The constant term multiplied in the above transformation comes to be
`(1)/(3)` which is
`<1`, which means that the transformation would be a horizontal stretch by a factor of 3.