Question

How do you graph, find the zeros, intercepts, domain and range of `f(x)=abs(4x)`?

Answer 1

Graph: A straight line from the origin of slope 4, with a miror reflection about the `y` axis.
`f(0)=0`, Domain: `(-oo, +oo)`, Range: `(0, +oo)`

Explanation:

`f(x) =abs(4x)`

`f(x) =4x` for `x>0` [A straight line from the origin of slope 4]
and
`f(x) =-4x` for `x<0` [A straight line from the origin of slope -4]
and
`f(x) =0` for `x=0` [The single zero and intercept of `f(x)`]

`f(x)` is defined `forall x ->` The domain of `f(x)` is `(-oo, +oo)`

`f(x) >=0 forall x ->` The range of `f(x)` is `(0, +oo)`

These can be seen from the graph of `f(x)` below:

graph{abs(4x) [-11.21, 11.29, -2.145, 9.105]}