Rational Functions Worksheet
Name:
Instructions: The model used to investigate the interesting parts of a rational function
is outlined in the steps for each problem.
1. Graph the rational function r(x) =
−5(x + 6)(x + 4)
.
3(x − 2)(x + 2)(x2 + 3)
Implied Domain This is a set that looks like R − {−2, 2}.
Vertical Asymptotes Find the roots of the demonator. (Some rational functions may
not have any.)
The roots are x =
and x =
Draw vertical dashed lines through these numbers.
x-intercepts Find the roots of the numerator. (Some rational functions may not have
any.)
The roots are x =
and x =
The x−intercepts are (
, 0) and (
, 0) Mark these points.
In between x−intercepts and vertical asymptotes. Choose numbers between consecutive pairs and test them in r(x). Check if the function is positive or negative.
c
r(c)
Far left and far right Compare the leading terms. r(x) is like
Put it together
+ or - ?
−5x2
5 1
=− 2
4
3x
3x
2. Graph the rational function
3(x2 + 1)(x2 + 3x + 1)
−2(x − 3)(x − 3)(x + 1)
Implied Domain:
Vertical Asymptotes:
x-intercepts:
In between x−intercepts and vertical asymptotes:
Far left and far right:
Put it together: