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## Calculus, all content (2017 edition)

### Unit 1: Lesson 3

Limits from graphs

# Limits from graphs: function undefined

Sal finds the limit of a function given its graph. The function isn't defined at the limiting value but that doesn't mean the limit doesn't exist!

## Video transcript

- [Voiceover] So we have the graph of y equal f of x right over here, and what we want to do is figure out the limit of f of x as x approaches negative four. So what does that mean? Well, a limit is saying, "What does my function approach "as the input of that function approaches, "in this case, negative four? "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 of negative four, you go to x equals negative four, and you see that f of negative four 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. And actually it can 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. What's going on as x approaches negative four? As x approaches negative four from values greater than negative four and from values less than negative four. Well let's first think about values greater than negative four. So when x is negative one, this is f of negative one. This is f of negative two, this is f of negative three. This is f of negative 3.5, this is f of negative 3.9, this is f of negative 3.99, this is f of negative 3.99999. And so you can see the value of our function, as x gets closer and closer to negative four from values greater than negative four, seems to be approaching six. And let's see if that's true from the other direction, so from values less than negative four. So this f of negative seven, f of negative six. This is f of negative five, puts us around seven. This is f of negative 4.5, f of negative 4.1, f of negative 4.01, f of negative 4.00001, it looks like it's getting awfully, it's going to be a little bit more than six, so it seems as we get closer and closer to x equal negative four, the value of our function is approaching positive six.