Chapter 2 Final Exam Review- Rational Fucntions

RATIONAL FUNCTIONS:

A rational function can be written in the form:

f(x)=N(x) / D(x)

- where N(x) and D(x) are polynomials

-From rational functions you can find vertical asymptotes, horizontal asymptotes, and the intercepts. You can then graph the function using this information.

Finding vertical asymptotes:

The line x=0 is a vertical asymptote.
Vertical asymptotes occur at the zeros of D(x).

Example:

f(x)= 2x/ x-3

VA: Set the denominator equal to 0 to find the zeros at D(x).

x-3=0
x=3
Vertical asymptote:  x=3   (dont forget to include the "x=" portion!)

Finding horizontal asymptotes:

The line y=0 is a horizontal asymptote.
Horizontal asymptotes can be found by observing the coefficents of the leading term of N(x) and D(x).

H.As exist in these conditions:

1- If the degree of the numerator is equal to the degree of the denominator 
**Take ratio of leading coefficents to find the H.A.

2- If the degree of the denominator is greater than the degree of the numerator
***y=0 is the H.A.

If the degree of the numerator is greater than the denominator there is no H.A.

Finding x and y intercepts:

Find x intercepts by setting y to zero 

Find y intercepts by setting x to zero

To graph:

Sketch the Vertical and Horizontal asymptotes and the x and y intercepts and sketch a corresponding graph. The graph should intersect at points of intersection and head off in the direction of positive or negative infinity in relation to the asymptotes. 

(see below videos for examples)

Here are some helpful videos on rational functions and their graphs:

Rational functions in general-

Graphing rational functions:

Finding x and y intercepts: 

Good luck studying!!