Question

How do you graph `f(x)=abs(x-2)+ 3`?

Answer 1

Note that `x=2` is a critical point of the function `f(x)` since for `x<2` the absolute value operation reverses the sign and for `x>2` the absolute value function has no effect.

Evaluate f(x) for `x=0` and for one value `<2` (say `x=0`) and for one value `>2` (say `x=4`)

`f(0) = 5`
`f(2) = 3`
`f(4) = 5`

draw a line from `(2,3)` (the critical point) through `(0,5)`
and
a second line from `(2,3)` (the critical point) through `(4,5)`
graph{|x-2|+3 [-5.03, 7.46, 0.4, 6.64]}