functions where the graph has vertical asymptotes, algebra homework help

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page 477 attached 8-3Graphing Rational Functions
GET READY for the Lesson
Main Ideas
с
150
1 student could
pay $150
• Determine the
limitations on the
domains and ranges
of the graphs of
rational functions.
125
100
A group of students want to get their
favorite teacher, Mr. Salgado, a
retirement gift. They plan to get him a
gift certificate for a weekend package at
a lodge in a state park. The certificate
costs $150. If c represents the cost for
each student and s represents the
150
number of students, then c=
S.
Cost (dollars)
25 students could
each pay $6.
75
• Graph rational
functions.
50
150 students could
each pay $1.
25
New Vocabulary
S
0
25 50 75 100 125 150
Students
rational function
continuity
asymptote
point discontinuity
=
Domain and Range The function c =
150
is a rational function. A
rational function has an equation of the form f(x)
p(x)
where p(x) and
g(x) are polynomial functions and g(x) = 0. Here are other rational
functions.
5
f(x) =
X +4
x + 3
X-
(x – 1)(x + 4)
X
h(x) =
No denominator in a rational function can be zero because division by
zero is not defined. The functions above are not defined at x = -3, X = 6,
and x = 1 and x = -4, respectively. The domain of a rational function is
limited to values for which the function is defined.
The graphs of rational functions may have breaks in continuity. This
means that, unlike polynomial functions, which can be traced with a
pencil never leaving the paper, not all rational functions are traceable.
Breaks in continuity occur at values that are excluded from the domain.
They can appear as vertical asymptotes or as point discontinuity. An
asymptote is a line that the graph of the function approaches, but never
touches. Point discontinuity is like a hole in a graph.
Vertical Asymptotes
Model
Example
For f(x) = x^31
f(x)
KEY CONCEPT
Property Words
Vertical If the rational
Asymptote expression of a
function is written
in simplest form
and the function is
undefined for
X = a, then the line
x = a is a vertical
asymptote.
the line x = 3 is
a vertical
asymptote.
f(x) =
o
Lesson 8-3 Graphing Rational Functions 457