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.

Common denominators: 1/4 and 5/6 | Math | 4th grade | Khan Academy

Safari Live - Day 214 | National Geographic

View All

See Why Jumping in a Pool Saved This Blind Woman's Life | Short Film Showcase

My first time in the pool, I was 49 years old. My coach was in the water telling me, “Jump in, Vivian,” he said. “Haven’t you been baptized?” I said, “Not like this.” I was afraid of what was going to happen to me in all this water. The kids said, “Look a…

Using the Teacher Skills Report to drive differentiation on Khan Academy

Today, I will show you how to use the skills overview report in the teacher dashboard on Khan Academy. Once you have logged into Khan Academy, go to your teacher dashboard. Once you are in your teacher dashboard, on the left-hand panel under Tools, click …

Re: The Trouble With The Electoral College – Cities, Metro Areas, Elections and The United States

Hello, internet. Let’s talk about this map, this argument, and the Electoral College in general. In my “Trouble With The Electoral College” video from 2011, I was wrong to use the city limits for that part of the argument, rather than the more expansive m…

Charlie Munger: This One Thing Helped Me Become a Billionaire

Warren and I, we never tried to make money out of the dumb, say, out of the stupidity of our dumb buyers. We tried to make money by buying, and if we were selling horse [ __ ], we didn’t want to pretend it was a cure for arthritis. And I think it’s better…

Western MBA 1980 Five Years Out Trailer mp4

I think the common experience of working through this extremely demanding program and working through it in groups produces relationships and friendships that last people throughout their entire management career. You see an interesting thing happening at…

Captain Cook Snags a Big Tuna | Wicked Tuna | National Geographic

Getting anything better down there, Johnny? A lot of bent rods. So we’re just getting set up right now on the Regal Sword. We made the move down from Crab Ledge last night. Might just set up right in here. Yeah. You know, you just get panic in panic mode…

Graphical limit where function undefined

More Articles