# How do you graph  y= abs( x - 4 ) + 1 ?

May 7, 2015

To graph $y = | x - 4 | + 1$, make a table of values, making sure to include positive and negative values for $x$. The graph will be in a v shape. The vertex will be where the absolute value is 0, |x-4|, where the $x = 4$, at which point $y = 1$. So the vertex is at $\left(4 , 1\right)$.

Table of Values
$\textcolor{g r e e n}{x} , \textcolor{p u r p \le}{y} = | x - 4 | + 1$

$\textcolor{g r e e n}{x} = \textcolor{red}{- 2} , \textcolor{p u r p \le}{y} = | - 2 - 4 | + 1 = \textcolor{b l u e}{7}$

$\textcolor{g r e e n}{x} = \textcolor{red}{- 1} , \textcolor{p u r p \le}{y} = | - 1 - 4 | + 1 = \textcolor{b l u e}{6}$

$\textcolor{g r e e n}{x} = \textcolor{red}{0} , \textcolor{p u r p \le}{y} = | 0 - 4 | + 1 = \textcolor{b l u e}{5}$

$\textcolor{g r e e n}{x} = \textcolor{red}{1} , \textcolor{p u r p \le}{y} = | 1 - 4 | + 1 = \textcolor{b l u e}{4}$

$\textcolor{g r e e n}{x} = \textcolor{red}{2} , \textcolor{p u r p \le}{y} = | 2 - 4 | + 1 = \textcolor{b l u e}{3}$

$\textcolor{g r e e n}{x} = \textcolor{red}{3} , \textcolor{p u r p \le}{y} = | 3 - 4 | + 1 = \textcolor{b l u e}{2}$

$\textcolor{g r e e n}{x} = \textcolor{red}{4} , \textcolor{p u r p \le}{y} = | 4 - 4 | + 1 = \textcolor{b l u e}{1}$

$\textcolor{g r e e n}{x} = \textcolor{red}{5} , \textcolor{p u r p \le}{y} = | 5 - 4 | + 1 = \textcolor{b l u e}{2}$

$\textcolor{g r e e n}{x} = \textcolor{red}{6} , \textcolor{p u r p \le}{y} = | 6 - 4 | + 1 = \textcolor{b l u e}{3}$

graph{y=|x-4|+1 [-16, 16.06, -7.87, 8.16]}