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.

Aoife O'Sullivan: Expert Aviation Lawyer Reveals All

Calculating change in spending or taxes to close output gaps | AP Macroeconomics | Khan Academy

View All

Elements and atomic number | Atoms, isotopes, and ions | High school chemistry | Khan Academy

We know that everything in the universe is composed of atoms, but not all atoms are the same. There are many different types of atoms called elements, each with a unique set of physical and chemical properties. Many elements are probably familiar to you; …

Worked example: Chain rule with table | Derivative rules | AP Calculus AB | Khan Academy

The following table lists the values of functions f and g and of their derivatives f prime and g prime for the x values negative 2 and 4. And so, you can see for x equals negative 2, x equals 4, they give us the values of f, g, f prime, and g prime. Let …

Voter turnout | Political participation | US government and civics | Khan Academy

What we’re going to talk about in this video is voter turnout, which is a way of thinking about how many of the people who could vote actually do vote. It’s often expressed as a number, as a percentage, where you have the number who vote over the number o…

Could Biking in a City Be Bad for Your Health? | National Geographic

Air pollution is bad for you, and we know that exercise is good for you. But there’s this unanswered question: is exercising in close proximity to traffic enough of a bad thing for you that we should be recommending separating biking lanes from traffic al…

Catalysts | Reaction rates and equilibrium | High school chemistry | Khan Academy

In this video we’re going to talk a little bit about catalysts. So let’s first imagine that we have two reactants, and I’m going to simplify things with these overly simplified drawings. So let’s say you have this reactant right over here, and I’m drawin…

Sun Tzu | How to Fight Smart (The Art of War)

This video doesn’t condone violence or war of any kind, but simply explores the tactics from an ancient text, and how these might work in everyday (non-military) settings in the modern world. Nevertheless, some information and graphics in this video could…

Graphical limit where function undefined

More Articles