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.

This week, we looked at what absolute values were. Absolute values are the distance that the number is from zero. In class, we used the analogy of attempting to throw crumpled paper balls into a garbage bin. One person made the shot, others missed and landed a certain distance from the trash can. While some paper balls will have landed in different positions, their distance from the trash can could be the same as another paper ball. Absolute values are written like so:

|-5| = 5

The answer is 5 because -5 is 5 away from 0.

|5| = 5

The answer is also 5 because 5 is 5 away from -5.

Numbers beside these terms act as coefficients. Like so:

3|-5|

3×5

=15

Or if there is an expression within the lines, you do those first before completing the equation:

3|-3+6|

3|3|

3*3

= 9

You can almost think of the lines like brackets.