explain how rational functions can be used when buying a group gift, assignment help

Use the information on

page 477

to explain how rational functions can be used when buying a group gift. Explain why only part of the graph of the rational function is meaningful in the context of the problem.

8-3
Graphing Rational Functions
Main Ideas
СІ
150
1 student could
pay $150
125
• Determine the
limitations on the
domains and ranges
of the graphs of
rational functions
• Graph rational
functions
GET READY for the Lesson
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 represents the
number of students, then c=-
100
Cost (dollars)
75
25 students could
eath này
150 students could
each pay $1.
50
25
150
New Vocabulary
0
25 50 75 100 125 150
rational function
Students
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()
9()
where p(x) and
9(x) are polynomial functions and g(x) +0. Here are other rational
functions.
h(x)
8(x) = 6
I+ 4
(x – 1)(x + 4)
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.
KEY CONCEPT
Vertical Asymptotes
Property
Example
If the rational
Asymptote expression of a
f
function is written
the line x = 3 is
a vertical
in simplest form
and the function is asymptote.
undefined for
x=0, then the line
x = a is a vertical
asymptote.
Words
Model
Vertical
For f(x) – 2-3
O
Lesson 8-3 Graphing Rational Functions 457