How do you graph #y<=absx#?

Question

1403 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-23T00:27:42

See below

#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 · 2017-06-23T00:38:24

See below:

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}