Question

How do you graph `f(x)=abs(x-3)+4`?

Answer 1

Actually there are two graphs

`f(x)=(x-3)+4=x+1`
for all values of `x>=3`
and:
`f(x)=-(x-3)+4=-x+7`
for all values of `x<=3`

The `x=3` is important, as at that point `x-3` becomes negative and must be "saved" by the `abs`-function.

At the value of `x=3` the two functions meet at `(3,4)`
graph{abs(x-3)+4 [-28.88, 28.85, -14.43, 14.45]}