Rational Functions, algebra homework help

1. OPEN ENDED Write a function where the graph has vertical asymptotes located at x = -5 and x = 2.
2. OPEN ENDED Write a rational equation that can be solved by first multiplying each side by 5(a + 2).
3. Writing in Math 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.

High
Graphing Rational Functions
GET READY for the Lesson
C
150
1 student could
pay $150
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 o
Cost (dollars)
25 students could
each pay $6.
75
50
150 students could
each pay $1.
25
0
25 50 75 100 125 150
Students
912)
Domain and Range The function c = 13° is a rational function. A
P(x)
rational function has an equation of the form f(x) = where p(x) and
9(x) are polynomial functions and g(x) + 0. Here are other rational
functions.
T +4
g(x) =
(x
5
Y
f(x)= 7+3
h(x) = 6 – 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 r= -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
is like a hole in a graph.