Question

How do you graph `y>=abs(x-1)-2`?

Answer 1

This is an absolute value inequality, so it's going to have a V shape.

Explanation:

The -1 inside the absolute value will shift it RIGHT by one unit. It may seem like you'd shift it left, but that is incorrect.

The -2 will shift it down 2 units.

So, the vertex will be at (1,-2)

Then, for the inequality, I like to use the origin (0,0) for my test point. Substitute 0 for both x and y in the inequality.

That gives `0 ge abs{-1}-2->0ge1-2->0ge-1`

Then, you need to determine if 0 is greater than or equal to -1. Since it is, that means the point (0,0) will be included in your shading.