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

Jul 20, 2017

The graph looks like this:

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

Explanation:

The absolute value function $y = \left\mid x \right\mid$ 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 $y = \left\mid x \right\mid - 2$, 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 $\left(0 , 0\right)$, so on the new graph it will be $\left(0 , - 2\right)$.

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 $\left(0 , 2\right)$ and connect it to $\left(0 , 2\right)$. Let's use $x = - 2$ and $x = 2$.

$y = \left\mid - 2 \right\mid - 2 = 2 - 2 = 0$

$y = \left\mid 2 \right\mid - 2 = 2 - 2 = 0$

So now we know the points $\left(- 2 , 0\right)$ and $\left(2 , 0\right)$ 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]}