October 26, 2015
Obj: To describe the graphs of rational functions, identify
horizontal and vertical asymptotes, and predict the end
behavior.
Find the domain and use limits to describe its behavior at
values of x not in its domain.
f(x) =
1
x-3
October 26, 2015
Obj: To describe the graphs of rational functions, identify
horizontal and vertical asymptotes, and predict the end
behavior.
Describe the transformations made to f(x) =
1. g(x) = 2
x+3
2. h(x) = 3x - 7
x-2
1
x
.
October 26, 2015
Graph of a Rational Function
Obj: To describe the graphs of rational functions, identify
horizontal and vertical asymptotes, and predict the end
behavior.
1. Horizontal/End behavior asymptote:
N = numerator degree
One of 3 possibilities can happen:
D = denominator degree
N<D
then horizontal asymptote is y = 0
N=D
then horizontal asymptote is y =
N>D
then no horizontal asymptote, but a slant/quotient
asymptote: y = q(x)
leading coef. of numerator
leading coef. of denominator
2. Vertical asymptotes: occur at zeros of denominator,
provided they are not also zeros of
the numerator.
3. x-intercepts: zeros of numerator, provided they are not
also zeros of the denominator.
4. y-intercept: the value of f(0), if defined.
October 26, 2015
Graph f(x) =
x+2
x2 + 3x + 2
Obj: To describe the graphs of rational functions, identify
horizontal and vertical asymptotes, and predict the end
behavior.
October 26, 2015
Obj: To describe the graphs of rational functions, identify
horizontal and vertical asymptotes, and predict the end
behavior.
Graph.
f(x) = 2x2 - 2
x2 - 4
October 26, 2015
Obj: To describe the graphs of rational functions, identify
horizontal and vertical asymptotes, and predict the end
behavior.
Graph.
f(x) =
x3
x2 - 9
October 26, 2015
Obj: To describe the graphs of rational functions, identify
horizontal and vertical asymptotes, and predict the end
behavior.
Graph f(x) = x - 3x +33x + 1
x-1
2
October 26, 2015
HW:
Obj: To describe the graphs of rational functions, identify
horizontal and vertical asymptotes, and predict the end
behavior.
HR: (2.6) Pg. 225: 1-7odd, 11-18, 37-43odd