This week was absolute values! An absolute value describes how far a number is from zero. When a question asks for an absolute value, it looks like this: |6|

Not that hard. How far is the number six from zero? Well, six. What about |-5|?

|-5| = 5 because -5 is five away from zero. That’s all there is to it.

Now, how do we graph an absolute value? A rule that should be remembered is that there will never be a part of your graph below the x-axis. If your graph is below the x-axis, that means your number is negative, which is wrong. Because absolute values are never negative.

Below is a table and a graph for the function y = x + 1 and y = |x + 1|.

See how the line practically bounces off of the x-axis? This is how an absolute value looks when it is graphed. The red line represents y = |x + 1| and the black line shows what the line would look like if we weren’t looking for the absolute value. The black line is y = x + 1.