# Video: Finding the One-Sided Limit of a Function from Its Graph at a Point If the Limit Exists

Determine lim_(𝑥 → −5⁺) 𝑓(𝑥).

01:49

### Video Transcript

Determine the limit as 𝑥 tends to negative five from above of 𝑓 of 𝑥.

We are given a graph of the function 𝑓 of 𝑥. And we can see that at negative five, that seems to be an asymptote. And therefore, the function 𝑓 of 𝑥 is undefined at 𝑥 equals negative five, but we’re looking for the limit as 𝑥 tends to negative five from above. The little plus sign tells us that we’re only considering values of 𝑥, which are greater than negative five. We’re getting closer and closer to negative five from above.

Looking back to the graph, we can see that 𝑓 of negative four is negative one. 𝑓 of negative 4.5 appears to be negative two. And as 𝑥 gets closer and closer to negative five, always remaining however greater than negative five, we can see that the value of 𝑓 of 𝑥 decreases.

And as there is an asymptote there, in fact it will continue to decrease without bound. So it will go past negative a million, then negative a billion, negative a trillion. Every real number will be passed.

So the limit as 𝑥 tends to negative five from above of 𝑓 of 𝑥 can’t be any real number because as 𝑥 gets closer to negative five, eventually the value of 𝑓 of 𝑥 will become smaller than any number you could name.

Another way of saying this, a shorthand for this is that the limit as 𝑥 tends to negative five from above of 𝑓 of 𝑥 is equal to negative infinity. This doesn’t mean that negative infinity is being considered as a number; this is just a shorthand for the statement we talked about before, which is that as 𝑥 gets closer and closer to negative five from above, 𝑓 of 𝑥 decreases without bound.