Question

How do you graph `y = - absx+ 2`?

Answer 1

It should look like the graph below:

graph{-abs(x)+2 [-10, 10, -5, 5]}

Explanation:

Graphs using an absolute value have 'corners' near where the value inside the bars changes sign. in this case, the 'corner' appears at x=0.

Normally, `y=abs(x)` gives an upward v-shape like so:
graph{abs(x) [-10, 10, -5, 5]}

However, the negative sign flips the graph over:

graph{-abs(x) [-10, 10, -5, 5]}

Finally, the addition of the +2 shifts the graph 2 units up:

graph{-abs(x)+2 [-10, 10, -5, 5]}

This can be shown in a table:

x y
-5 -3
-3 -1
-1 1
0 2
1 1
3 -1
5 -3