Question

Given that (6,-3) is on the graph of f(x), find the corresponding point for the function f(1/3x)

Answer 1

The corresponding point for the function
`f((1)/(3)x)` is

(18, -3)

Explanation:

By definition if we have a function f(x) and we apply the transformation:

`y = f (hx)`

Then:

If
`0 <h <1` the graph is stretched horizontally by a factor
`(1)/(h)`

If
`h> 1` the graph is compressed horizontally by a factor
`(1)/(h)`

In this case
`h=(1)/(3)` this is
`0 <h <1` then the graph is stretched horizontally by a factor
`(1)/((1)/(3))=3`

Therefore the point (6, -3) that belongs to f(x), in the transformed function will be (3*6, -3) This is (18, -3)

Observe the example shown in the attached image