Section 3.7 Rational Functions
A rational function is a function of the form
r ( x) =
P ( x)
Q( x)
where P and Q are polynomials.
Rational Functions and Asymptotes
The domain of a rational function consists of all real numbers x except those for which the
Section 2.2 Graphs of Functions
DEFINITION: A function f is a rule that assigns to each element x in a set A exactly one
element, called f (x), in a set B . Its graph is the set of ordered pairs
cfw_(x, f (x) | x A
EXAMPLE:
Sketch the graphs of the follow
Section 2.3 Getting Information from the Graph of a
Function
Increasing and Decreasing Functions
DEFINITION: A function f is called increasing on an interval I if
f (x1 ) < f (x2 ) whenever x1 < x2 in I
It is called decreasing on an I if
f (x1 ) > f (x2 )
Section 2.1 What Is a Function?
DEFINITION: A function f is a rule that assigns to each element x in a set A exactly one
element, called f (x), in a set B . The set A is called the domain of f. The range of f is the
set of all possible values of f (x) as
Section 2.4 Average Rate of Change of a Function
Suppose you take a car trip and record the distance that you travel every few minutes. The
distance s you have traveled is a function of the time t:
s(t) = total distance traveled at time t
We graph the fun