Week 7: Rational Functions

The blog topic for this week is Rational Functions. We looked at this in Algebra 2 and it is when you use Vertical and Horizontal Asymptotes. 

Usually the equations would look like 

f(x)=P(x)/Q(x)

To find the Vertical Asymptotes of a problem you would set the denominator=0 and the answer would be x= the answer.

To find Horizontal Asymptotes of a problem, you look at the degree of the first equation:

It would look like

f(x)=anX^n/bmX^m.

n= degree of numerator

m= degree of denominator

an= L.C. of numerator

bm= L.C. of denominator

It would be like n/m

To find the horizontal asymptote though, there are three possibilites

When the degrees are both equal. n=m you would use the coefficient of both answers as the answer. If its 2/2 then it would be y=1

Then n<m the answer would be y=0

n>m then the answer DNE.

However, something we have not seen before is Slant Asymptotes which is only possible if the horizontal asymptote is n>m.

f(x)=m(x)/d(x)

The answer from the vertical asymptote is used to divide numerator of the equation. For example x=2 is the VA. You would divide it by its numerator, for example x^2+4. y= answer.

For all equations, there will be x-intercepts and y-intercepts. You just plug in zero for the opposite to find it. If looking for the x-intercept, make y=0 and solve and vice versa.

To find the holes in a problem. You factor the equation and see if anything can be canceled out. Whatever cancels out is the answer and it would usually look like (x,y). If nothing cancels out, there is no hole. 

Below is one example of how to solve a rational function.

This is how Rational Functions work.

See You Next Week!