Question

What is the graph of the absolute value function \[x=\left| y \right|\]?

Answer 1

Hint: In this problem, we have to graph the absolute value function \[x=\left| y \right|\]. We should know that absolute value is when any value we give to y is negative, it results in positive. Here we can first write the absolute value parent function for the given absolute value equation. We can then find some ordered pairs by assigning values to x.

Complete step by step solution:
Here we have to find the graph for the given absolute value function \[x=\left| y \right|\].
We should know that an absolute value function is a function that contains an algebraic expression within absolute value symbols.
We should know that absolute value is when any value we give to y is negative, it results in positive.
We can now write the absolute value parent function as \[x=\left| y \right|\]
\[\Rightarrow x=\left\{ \begin{matrix}
   y & if\text{ }y>0 \\
   0 & if\text{ }y=0 \\
   -y & if\text{ }y<0 \\
\end{matrix} \right.\]
We can now find some ordered pairs by choosing several values for y to plot the graph.
We can now take y = 1, the x is,
\[\Rightarrow x=\left| 1 \right|=1\]
We can take y = -1, the x is
\[\Rightarrow x=\left| -1 \right|=1\]
We can now take y = -2, then x is
\[\Rightarrow x=\left| -2 \right|=2\]
We can take y = 2, the x is
\[\Rightarrow x=\left| 2 \right|=2\]
Therefore, the ordered pairs to be plotted are \[\left( 1,1 \right),\left( 1,-1 \right),\left( 2,2 \right),\left( 2,-2 \right)\]
We can now plot the graph.

Note: We should always remember that the absolute value is when any value we give to y is negative, it results in positive. We should know that an absolute value function is a function that contains an algebraic expression within absolute value symbols.