Unit G Summary Question 3: Slant Asymptotes

When does a graph have a slant asypmtote? How do you find the equation of the slant asymptote?

A slant asymptote is a diagonal imaginary line that a graph approaches but should not touch. A graph has a slant asymptote when the degree of the numerator is one, exactly one, degree bigger than the degree on the denominator of a function. What this means is that if the x (or whatever variable) on the top of a function has one power more than the the x on the bottom, the graph has a slant asymptote. To find the equation of the slant asymptote, one divide the numerator by the denominator using long division. The equation will be your answer excluding the remainder.

Unit G Summary Question #2: H.A. - Limit Notation

Describe what limit notation for horizontal asymptotes actually means.

Don't tell me what to do! Limit notation for horizontal asymptotes looks like this:
as x --> infinity, f(x) -->__
as x --> -infinity, f(x) -->__
In the case of that graph above, that line next to the arrow would be 0. This means that as a graph goes to the right, it will approach but not touch that number for a y-value and it would mean the same for when it goes to the left. The limit notation for horizontal asymptotes is just a fancy mathematical way of saying what boundaries a graph has like a soccer player cannot go out of bounds if he wants to keep possession of the ball.

Unit G Summary Question #1: Horizontal Asymptotes

How do we know if a graph has a horizontal asymptote? What are the three options?

To answer this question, first I feel the need to define what a horizontal asymptote is. A horizontal asymptote is an imaginary horizontal line that a graph cannot touch like in the example above where that curved line got close to but did not cross the y=4 horizontal asymptote. We know if a graph has a horizontal asymptote when we see that a graph approaches a y-value but never actually reaches it in a graphing calculator or in a graph in general. Another way we know if a graph has a horizontal asymptote is when you find that you get a bigger degree on the bottom (the denominator) after you compare the degrees of the numerator and the denominator of a function. The third way is when both the numerator and denominator of a function have the same degrees.