College Algebra, Chapter 2, 2.2, Section 2.2, Problem 30

Make a table of values and sketch the graph of the equation $y = |x|$. Find the $x$ and $y$ intercepts.

By using the Property of Absolute Value,

$\begin{array}{cc}
y = x & y = -x \\
\end{array} $

$y = \left\{ \begin{array}{cc}
x & \text{for } x > 0 \\
-x & \text{for } x < 0
\end{array} \right.$

$
\begin{array}{|c|c|}
\hline\\
\text{Let } x & f(x) \\
\hline\\
-3 & 3 \\
\hline\\
-2 & 2 \\
\hline\\
-1 & 1 \\
\hline\\
1 & 1 \\
\hline\\
2 & 2 \\
\hline\\
3 & 3\\
\hline
\end{array}

$

To solve for $x$ intercept, where $y = 0$

$0 = x$

To solve for the $y$ intercept, we set $x = 0$

$y = 0$

Thus, the $x$ and $y$ intercepts are at $(0, 0)$