# How do you graph y=|x-1| +4?

Mar 7, 2018

See the explanation below

#### Explanation:

Start by graphing

$y = | x |$

The function is defined for $x \in \mathbb{R}$

$y = 0$ when $x = 0$

When $x > 0$, $y = x$

and

When $x < 0$, $y = - \left(x\right) = - x$

graph{|x| [-7.15, 8.654, -0.39, 7.51]}

Next graph,

$y = | x - 1 |$

The graph of $y = | x |$ is shifted one unit to the right

graph{|x-1| [-7.15, 8.654, -0.39, 7.51]}

And finally, graph

$y = | x - 1 | + 4$

The graph $y = | x - 1 |$ is shifted vertically by $4$ units.

graph{|x-1|+4 [-7.15, 8.654, -0.39, 7.51]}

Mar 7, 2018

#### Explanation:

Generate a few sample points,
one for which $\left\mid x - 1 \right\mid = 0$
and a couple for each of
$\textcolor{w h i t e}{\text{XXX")(x-1) < 0color(white)("xx")"and"color(white)("xx}} \left(x - 1\right) > 0$

The sample points I used were
color(white)("XXX"){: (color(white)("x")ul(x),color(white)("xxxx"),ul(y=abs(x-1)+4)), (color(white)("x")1,,color(white)("xxx")4), (color(white)("x")0,,color(white)("xxx")5), (-1,,color(white)("xxx")6), (color(white)("x")2,,color(white)("xxx")5), (color(white)("x")3,,color(white)("xxx")6) :}

Plot these points on the Cartesian plane
and draw straight lines extending from the vertex point (where $\left\mid x - 1 \right\mid = 0$) through each of the two sets of points.