Question

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

Answer 1

The graph looks like this:

graph{y=absx-2 [-10.125, 9.875, -5, 5]}

Explanation:

The absolute value function `y=absx` looks like this:

graph{y=absx [-9.875, 10.125, -3.68, 6.32]}

This is a function you should probably know well for the future. Anyway, in order to plot `y = absx - 2`, we need to shift the `y` values down by `2`, since we are subtracting two from what `y` is.

I would start graphing this graph by plotting the vertex (the point where the graph has a tight corner). On the original graph it is `(0,0)`, so on the new graph it will be `(0,-2)`.

graph{x^2+(y+2)^2<=.04 [-9.875, 10.125, -3.68, 6.32]}

Now you need to draw the two rays coming from this point. To do this, graph one point on either side of `(0,2)` and connect it to `(0,2)`. Let's use `x=-2` and `x=2`.

`y = abs(-2)-2 = 2 - 2 = 0`

`y= abs2-2 = 2-2 = 0`

So now we know the points `(-2,0)` and `(2,0)` are on our graph.

graph{(x^2+(y+2)^2-0.04)((x-2)^2+y^2-0.04)((x+2)^2+y^2-0.04) = 0 [-10.125, 9.875, -5, 5]}

Now all that you have to do is connect these points.

graph{y=absx-2 [-10.125, 9.875, -5, 5]}

Final Answer