Graphical limit where function undefined

2m read

·Nov 11, 2024

So we have the graph of ( y = f(x) ) right over here. What we want to do is figure out the limit of ( f(x) ) as ( x ) approaches -4. So, what does that mean?

Well, a limit is saying, “What is my function approaching as the input of that function approaches, in this case, -4?” As the input approaches a value, and as we see in this example, the function doesn't necessarily have to be even defined at that value. We can see ( f(4) ), you go to ( x ) at -4, and you see that ( f(4) ) is undefined. So this is not defined, but as we'll see, even though the function isn't defined there, the limit might be defined there.

Actually, it could go the other way around; sometimes a function is defined there, but the limit is not, and we'll see that in future videos. But let's just get an understanding here of what's going on as ( x ) approaches -4 from values greater than -4 and from values less than -4.

Well, let's first think about values greater than -4. So when ( x ) is -1, this is ( f(-1) ). This is ( f(-2) ). This is ( f(-3) ). This is ( f(-3.5) ). This is ( f(-3.9) ). This is ( f(-3.99) ). This is ( f(-4.0001) ). You can see the value of our function, as ( x ) gets closer and closer to -4 from values greater than -4, seems to be approaching 6.

Let’s see if that's true from the other direction, some from values less than -4. So this is ( f(-7) ). This is ( f(-5) ). This is ( f(-4.5) ). This is ( f(-4.1) ). This is ( f(-4.01) ). It looks like it's getting awfully close to a little bit more than 6. So it seems, as we get closer and closer to -4, the value of our function is approaching positive 6.

Multiplying 1-digit numbers by 10, 100, and 1000 | Math | 4th grade | Khan Academy

Doctor vs Plumber: Which person is WEALTHIER at Age 42

View All

Hershey and Chase conclusively show DNA genetic material

In the last video, we began to see some pretty good evidence that DNA was the molecular basis for inheritance. We saw that from the work of Avery, McCarthy, and Mlead, where they tried to identify whether it was DNA or proteins that acted as a transformat…

How costs change when fixed and variable costs change | APⓇ Microeconomics | Khan Academy

In the last few videos, we were studying our watch factory, ABC Watch Factory. Based on some data, knowing what our fixed costs are, our labor units, our variable cost, our total cost, and then our total output, and that would be for different amounts of …

What Happens AFTER Nuclear War?

Nuclear war would forever split human history. Into anything that happened before and the post-war apocalypse. In the worst case, mass fires consume everything within tens of thousands of square kilometers, killing hundreds of millions within hours. But t…

Worked example: limit comparison test | Series | AP Calculus BC | Khan Academy

So we’re given a series here and they say what series should we use in the limit comparison test. Let me underline that: the limit comparison test in order to determine whether ( S ) converges. So let’s just remind ourselves about the limit comparison te…

The Most Complex Language in the World

You are cells: your muscles, organs, skin, and hair. They are in your blood and in your bones. Cells are biological robots. They don’t want anything; they don’t feel anything. They are never sad or happy; they just are right here, right now. They’re as co…

Guided meditation for procrastination

Welcome to the meditation on procrastination. And somewhat ironically, I’ve been procrastinating making this meditation, so we’re all in the same boat together. So, as with all meditations, posture and breathing makes a big difference. I really encoura…

Graphical limit where function undefined

More Articles