Question

How does the graph of f(x)=4 cos(1/2x)-3 differ from the graph of g(x)=4 cos(x)-3

Answer 1

The graph of f(x)=4 cos(1/2x)-3 differs from the graph of g(x)=4 cos(x)-3, f(x) is stretched horizontally.

Answer 2

The function f(x) is stretched horizontally.

Explanation:

We are asked to determine how the graph of
`f(x)=4\text{cos}((1)/(2)x)-3` differ from the graph of
`g(x)=4\text{cos}(x)-3`.

Let us recall transformation rules of functions.

`f(ax)\rightarrow`

If
`a>1` function compresses horizontally.

If
`a<1` function stretches horizontally.

Upon looking at function
`f(x)=4\text{cos}((1)/(2)x)-3`, we can see that the value of 'a' is less than 1 that is
`(1)/(2)<1`, therefore, the function f(x) is stretched horizontally.