A close look at end behavior
- Charlie Barnes
- It oversimplifies the concept.
- It is a technique that encourages rote memorization, rather than conceptual understanding.
.I used polynomial long division there. So the in is called the quotient, and the is called the remainder (because goes into times with a remainder of ). Since , , and thus our rational function has a horizontal asymptote at .
Which type of rational function was this?
What is the quotient in a BOB0 rational function? Explain why that's consistent with the BOB0 rule.
.So the quotient is . Use the graph below to plot this rational function.
What you're seeing is that this function is asymptotic not to a horizontal line, but to the line . is what's called a slant asymptote of . Explain how BOTN oversimplifies this situation.