Chapter Three: Section Five

Limits at Infinity

Chapter Three: Section Five We have discussed in the past the idea of

functions having a finite limit as x approaches positive or negative infinity.

This situation results in a horizontal asymptote.

When can we tell if a function might have a horizontal asymptote?

Chapter Three: Section Five The visual clue we look for is to see if the function

is defined as a rational function.

We compare the ‘power’ of the numerator and the denominator of the rationally defined function.

Whenever the denominator grows at least as quickly as the numerator then the function has a horizontal asymptote.

Chapter Three: Section Five There is a major misconception about horizontal

asymptotes that we need to address here. It is possible for a function to cross its horizontal asymptote. In fact, a graph can cross its horizontal asymptote an infinite number of times.

Look at the graph on the next slide. Can you make a guess at a function that would have this graph?

Chapter Three: Section Five