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How do you graph #y<=absx#?

Answer 1

Savannah Anderson

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]}

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Answer 2

Avery Alexander

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}

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Answer 3

Savannah Anderson

To graph (y \leq |x|), follow these steps:

Graph the absolute value function (y = |x|).
Identify the portion of the graph where (y) is less than or equal to (|x|).
Shade the area below or on the graph of (y = |x|) to represent the solution to the inequality.

Let's proceed with graphing the function.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you graph #y&lt;=absx#?

How do you graph #y<=absx#?