This week in Pre-calc 11 we started learning about how to graph absolute values. The parent function that we used is . As we know from our past units, an absolute value is the distance of a number from 0 on the number line, meaning that there will never be a negative y-value.

We used our past knowledge of graphing to help us better understand how to graph an absolute value. For example, we already know how to graph equations like (1) or (2)

1

2

With these to non-absolute value equations, we can see that there are y values that are negative. Now, we add in the absolute value symbols to the equation and see the difference from the two graphs.

(1) and (2)

1

2

After adding in the signs, we can see the difference it makes. For the first graph, the line stopped at the x axis and bounced off it, therefore reflecting itself on the opposite side. The point where the line stops at the x-axis and bounces back up is called the critical point (similar to the vertex of a parabola.

For the second graph, we can see that when no negative y values are allowed, the negative vertex and some other negative points had to flip to the positive side to create a W shape.