3.3 Day 1 Rational Functions 2011
September 30, 2011
3.3 Rational Functions
(Day 1)
Objectives: Identify rational functions.
Find the domain of a rational function.
1
3.3 Day 1 Rational Functions 2011
September 30, 2011
Warm­up: Find a partner and a graphing calculator (to share). Sketch the graphs of each of the following functions.
1
2. y = x + 3
1
4. y = + 4
x ­ 1
1
1. y = x
3. y = ­ 2
x
1
5. How do h and k impact the graph of the function?
1
y = + k
x ­ h
2
3.3 Day 1 Rational Functions 2011
September 30, 2011
A rational function is a function of the form
p(x)
R(x) = q(x)
where p and q are polynomial functions and q is not the zero polynomial. The domain is the set of all real numbers excepts those for which the denominator equals zero.
3
3.3 Day 1 Rational Functions 2011
September 30, 2011
Find the domain of each rational function
4x
1) f(x) = x ­ 3
­4x2
2) g(x) = (x ­ 2)(x + 4)
4
3.3 Day 1 Rational Functions 2011
September 30, 2011
Use the graph to find:
a) the domain and range
b) the intercepts, if any
c) horizontal asymptotes
d) vertical asymptotes
5
3.3 Day 1 Rational Functions 2011
September 30, 2011
Use the graph to find:
a) the domain and range
b) the intercepts, if any
(­2, 0)
(2, 0)
c) horizontal asymptotes
d) vertical asymptotes
6
3.3 Day 1 Rational Functions 2011
September 30, 2011
HOMEWORK:
pg. 196 #'s: 12­22 even,
23, 24, 27, 28 a ­ d only
pg. 983 #'s: 5 ­ 9 7