# How do you graph y = 2 abs (x - 1 ) - 3?

Jul 23, 2015

Follow the instructions in the explanation.

#### Explanation:

Make a table of $x$ and $y$ values, making sure to include positive and negative values for $x$, and use a wide range of values for $x$.

$x = - 6 ,$ $y = 2 \left\mid - 6 - 1 \right\mid - 3 = 2 \left\mid - 7 \right\mid - 3 = 2 \left(7\right) - 3 = 11$
$x = - 5 ,$ $y = 2 \left\mid - 5 - 1 \right\mid - 3 = 2 \left\mid - 6 \right\mid - 3 = 2 \left(6\right) - 3 = 9$
$x = - 3 ,$ $y = 2 \left\mid - 3 - 1 \right\mid - 3 = 2 \left\mid - 4 \right\mid - 3 = 2 \left(4\right) - 3 = 5$
$x = - 1 ,$ $y = 2 \left\mid - 1 - 1 \right\mid - 3 = 2 \left\mid - 2 \right\mid - 3 = 2 \left(2\right) - 3 = 1$
$x = 0 ,$ $y = 2 \left\mid 0 - 1 \right\mid - 3 = 2 \left\mid - 1 \right\mid - 3 = 2 \left(1\right) - 3 = - 1$
$x = 1 ,$ $y = 2 \left\mid 1 - 1 \right\mid - 3 = 2 \left\mid 0 \right\mid - 3 = 2 \left(0\right) - 3 = - 3$
$x = 3 ,$ $y = 2 \left\mid 3 - 1 \right\mid - 3 = 2 \left\mid 2 \right\mid - 3 = 2 \left(2\right) - 3 = 1$
$x = 5 ,$ $y = 2 \left\mid 5 - 1 \right\mid - 3 = 2 \left\mid 4 \right\mid - 3 = 2 \left(4\right) - 3 = 5$
$x = 6 ,$ $y = 2 \left\mid 6 - 1 \right\mid - 3 = 2 \left\mid 5 \right\mid - 3 = 2 \left(5\right) - 3 = 7$

Table
$\textcolor{red}{x} | \textcolor{p u r p \le}{y}$
$\textcolor{red}{- 6} | \textcolor{p u r p \le}{11}$
$\textcolor{red}{- 5} | \textcolor{p u r p \le}{9}$
$\textcolor{red}{- 3} | \textcolor{p u r p \le}{5}$
$\textcolor{red}{- 1} | \textcolor{p u r p \le}{1}$
$\textcolor{red}{0} | \textcolor{p u r p \le}{- 1}$
$\textcolor{red}{1} | \textcolor{p u r p \le}{- 3}$
$\textcolor{red}{3} | \textcolor{p u r p \le}{1}$
$\textcolor{red}{5} | \textcolor{p u r p \le}{5}$
$\textcolor{red}{6} | \textcolor{p u r p \le}{7}$

Plot the points, and draw a straight line through both sides, with each side meeting at $\left(1 , - 3\right)$.

graph{y=2abs(x-1)-3 [-16.02, 16, -5.12, 10.9]}