The right arrow “” means “goes to” or “approaches”. Remember that this is essentially what the limit is already saying; so
saying is a little redundant. Indeed this would be translated to say “as x goes to -1, the function goes to ’goes
to infinity’.” Which isn’t quite right. So if you use the “” notation, then you should use an equals sign. If you
don’t, then you should use the “” to signify that the function is approaching a value, but not “equal” to a value.
We explore functions that “shoot to infinity” near certain points.
Video Lecture
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Consider the function
Which of the following are correct?
On the other hand, consider the function
Find the vertical asymptotes of
Since is a rational function, it is continuous on its domain. So the only points where the function can possibly have a vertical
asymptote are zeros of the denominator.
Start by factoring both the numerator and the denominator: Using limits, we must investigate what happens with when and , since and are the only zeros of the denominator. Write 
Hence we have a vertical asymptote at .
Start by factoring both the numerator and the denominator: Using limits, we must investigate what happens with when and , since and are the only zeros of the denominator. Write
Now write
Consider the one-sided limits separately.
When , the quantity is positive and approaches and the numerator is negative, therefore, .
On the other hand, when , the quantity is negative and approaches and the numerator is negative, therefore, .