Question

How does the graph of f(x) = 5
cos 1/2 X

Answer 1

The graph of
`f(x)=5\cos((1)/(2)x)` is a vertical stretch of 5 units and a horizontal stretch by 2 units of the parent graph

Explanation:

We want to find out how the graph of
`f(x)=5\cos((1)/(2)x)` compare with the graph of the parent function
`g(x)=\cos (x)`.

We can observe that the transformation applied to the basic cosine function is of the form:

`y=A \cos Bx`

The
`A=5` is a vertical stretch by a factor of 5 units.

`B=(1)/(2)` is a horizontal stretch by a factor of 2 units.

Therefore the graph of
`f(x)=5\cos((1)/(2)x)` will stretch vertically by a factor of 5 units and stretch horizontally by a factor of 2 units as compared to
`g(x)=\cos (x)`.

See attachment