Ok People, This Chapter Is a Hard One, but Don T Worry, I Will Explain All the Concepts

Ok people, this chapter is a hard one, but don’t worry, I will explain all the concepts and walk you through each example. So here are the things that you will be learning.

·  Vertical Asymptotes

·  Horizontal Asymptotes

·  “Holes” in graphs

·  How to graph a rational equation.

Ok, now lets cover the basics. An asymptote is a value that the graph will never touch. It will go SUPER close to this value, but still will not touch it. Never.

So, to start, to graph an equation, use this trick:

The BLUE number represents the vertical translations, (+/- )= (up/down)

The GREEN number represents the vertical stretch factor (+ or -)

The RED number is in the equation x-(k) is k is positive, than the translation is to the right, and if k is negative, the graph is moved left.

For example:

A vertical asymptote is defined as the following:

Did you get that? If not, then here is the straight explaination:

Ok, for example:

So, basically, the zeros of the denominator in the rational equation are the vertical asymptotes of the graph.

In this case, P is the numerator in a rational expression, and Q is the denominator.

·  If the degree of the numerator is less than the degree of the denominator, then the horizontal asymptote is definitely be y=0.

·  If the degrees of the numerator and the denominator are the same, the leading coefficients , aka, the coefficient of the variable w/ the highest exponent, the asymptote is equal to the fraction of the two, you will se an example.

·  If the degree of the numerator is greater than the degree of the denomiator, then there is no horizontal asymptote.

Example:

Figure 1 This is the graph, look closely, the graph never touches the y=1 line, it never will.

You may think that this title is funny, infact, you may be laughing at it right now and pointing it out to your friends, yes, I think that you are. And I’m probably right, now, to get on w/ this…

It is simple:

So when you fully factor both the numerator and the denominator, you might get a factor that goes into both the numerator and denominator, and the zero for that factor is the “hole” in the graph, no matter the type in this section. For example:

And so the “hole” would be at x=1.

Now rate this guide, I can make it better, tell me how.