Question

How do you graph `y<=absx`?

Answer 1

See below

Explanation:

`y=abs(x)` looks like this:

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

Since they want `y<=abs(x)`, we just need to shade that region in.

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

Look what `y>=abs(x)` looks like:

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

Answer 2

See below:

Explanation:

Let's first graph the line `y=absx` and then work out the `le` part of it.

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

`abs1=abs(-1)=1`

That gives us the graph of `y=absx` 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, absx=1`, and so `y=-1 le abs(-1)`. We therefore shade under the line:

graph{y-absx<=0}