Question

how would you describe the graph for the equation |x|=2

Answer 1

Remember that from the definition of modulus we have

$|x|=\begin{cases}x,x>0 \\ -x,x<0\end{cases}$

Therefore, it's always a positive value!

If we have

$|x|=2$

The values of x are

$\begin{gathered} x=+2 \\ x=-2 \end{gathered}$

Because

$\begin{gathered} |-2|=2 \\ |2|=2 \end{gathered}$

Therefore, the graph of that solution would be a CLOSED circle on the -2 and a CLOSED circle on the 2, we always use a closed circle to represent a solution.