# How do you graph y=-abs(x-8)+1?

Nov 29, 2017

See below

#### Explanation:

$y = - \left\mid x - 8 \right\mid + 1$

When approaching a graphing problem of this nature it may be easier to consider the following steps.

Step 1. The graph of $\left\mid x - 8 \right\mid$ is the 'V-graph' formed as follows:

$f \left(x\right) = - \left(x - 8\right)$ for $x \in \left(- \infty , 8\right)$
$f \left(8\right) = 0$
$f \left(x\right) = + \left(x - 8\right)$ for $x \in \left(8 , + \infty\right)$

Step 2. The graph of $- \left\mid x - 8 \right\mid$ is the mirror reflection of the graph in Step 1 about the $x -$axis

Step 3. The graph of $- \left\mid x - 8 \right\mid + 1$ is the graph from Step 2 transformed ("shifted") 1 unit positive ("up") on the $y -$axis.

The resultant graph of $y$ is shown below.

graph{-abs(x-8)+1 [-0.65, 11.84, -3.324, 2.92]}