chapter 3 summary

In chapter three, we learned about rational zeros, rational functions, divisions and asymtopes.  The chapter was not extremely hard to me, it is just a little tidious when doing some steps.  When we are given a function and a zero or factor, we use division to find the other zeros. The power of the first x term indicates the number of zeros.  When the problem asks me to complete the factorization, I divide all the given zeros or factors to get the equation into x square form. We need to put the answer into the form of q(x)•d(x)+r(x).  I liked this chapter eventhough I think I did bad on the test.  

Rational functions

Rational functions are a polynomial over a polynomial. It looks really complicated,but when we take it down into pieces, it is actually easy to graph.   In order to graph the functions, we need to find three things. First, the horizontal,slant and vertical asymtopes, secondly, holes, if the graph has any. To find the vertical asymtopes, we set the denominator to zero and solve for x. To find the horizontal one, we have to test if the value of n is larger than m, if it is, there's no horizontal asymtopes. If n<m! the answer would be y=an/bm. If they are equal, the answer is y=0.  We divid the functions using long division I order to find the slant asymtopes. It only exists if n>m.  We factor and cancel to find the holes, and the answer should be a ordered pair.