Department of Mathematics
Theory
Precalculus 
by Example
Series
Rational Functions


Polynomial and Rational Functions

Question 1 - Find the Domain and Range of the following rational function:

(a) 

(a) , So zeros are x = -½ and x = 2, y-intercept is -2

Sketch looks like: Domain:  Range: y > 0 and 
 

Question 2. Sketch the following function and clearly state all y-intercept, x-intercepts,
vertical and horizontal asymptotes:


 
 

Can be written as: 

So vertical asymptotes at x = -3 and x = +3 (when denominator = 0)

There is a horizontal asymptote at y = 2

Zeros at x= -1 and x = +1 (when numerator = 0)

y-intercept at (0, 0.2), or when x = 0 y =