Question

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

Answer 1

Graph the linear segment for `x>=3` then add the linear segment for `x < 3`

Explanation:

Part 1: `x >= 3`
when `x>= 3`
`f(x) = abs(x-3)` is equivalent to `f(x)=x-3`
Two or three data points will be sufficient to plot and verify this half of the graph
#color(white)("XXX") {: (x,color(white)("XX"),f(x)), (3,color(white)("XX"),0), (4,color(white)("XX"),1), (5,color(white)("XX"),2) :}#

Part 2: `x < 3`
when `x < 3`
`f(x)= abs(x-3)` is equivalent to `f(x) = 3-x`
Again, two or three data points will be sufficient to plot and verify this second half of the graph
#color(white)("XXX") {: (x,color(white)("XX"),f(x)), (2,color(white)("XX"),1), (1,color(white)("XX"),2), (0,color(white)("XX"),3) :}#
graph{abs(x-3) [-1.673, 8.192, -0.545, 4.388]}