# How do you graph y<=absx?

Jun 23, 2017

See below

#### Explanation:

$y = \left\mid x \right\mid$ looks like this:

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

Since they want $y \le \left\mid x \right\mid$, we just need to shade that region in.

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

Look what $y \ge \left\mid x \right\mid$ looks like:

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

See below:

#### Explanation:

Let's first graph the line $y = \left\mid x \right\mid$ and then work out the $\le$ part of it.

The absolute value function returns a positive value of what is inside. And so:

$\left\mid 1 \right\mid = \left\mid - 1 \right\mid = 1$

That gives us the graph of $y = \left\mid x \right\mid$ as:

graph{absx}

Now let's figure out which side of the line is the solution set and should be shaded.

We know that when $x = - 1 , \left\mid x \right\mid = 1$, and so $y = - 1 \le \left\mid - 1 \right\mid$. We therefore shade under the line:

graph{y-absx<=0}