Question

Use f(x) = |x| to describe the following transformations. 3) j(x) = 3f(x)

Answer 1

The transformation

`f(x)\longrightarrow j(x)=3f(x)`

describes a vertical stretch by a factor of 3 as we can note on the following picture:

A vertical compression occurs when the factor is between 0 and 1, for instace, if the factor is 1/4 instead of 3, we have the purple graph g(x):

In the case m(x) =f(3x), we have

`m(x)=|3x|`

which is equivalent to

`m(x)=3|x|`

then, in this particular case, the graphs of 3f(x) and f(3x) will be the same.