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

##### 1 Answer
Aug 31, 2015

Graph the linear segment for $x \ge 3$ then add the linear segment for $x < 3$

#### Explanation:

Part 1: $x \ge 3$
when $x \ge 3$
$f \left(x\right) = \left\mid x - 3 \right\mid$ is equivalent to $f \left(x\right) = x - 3$
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 $x < 3$
$f \left(x\right) = \left\mid x - 3 \right\mid$ is equivalent to $f \left(x\right) = 3 - x$
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]}