help with Rational Functions, algebra homework help

Rational Functions End Checkpoint Apply

Lessons 3 – 4

Please complete the following questions. It is important that you show all work you did to solve the problems when you submit your work. This includes any calculations, diagrams, or graphs that helped you solve it.

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 (attached below) 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.

100%
150
1 student could
pay $150
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 s represents the
number of students, then c = ”
150
Cost (dollars)
125
100
75
25 students could
each pay $6.
150 students could
each pay $1.
50
25
S
0 25 50 75 100 125 150
Students
Domain and Range The function c = 150 is a rational function. A
rational function has an equation of the form f(x) = P(r)
where p(x) and
9(x) are polynomial functions and g(x) + 0. Here are other rational
functions.
f(x) = x + 3
8(x) = 56 1(x)
x + 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.