Chapter 2 Lesson 2 Rational Function

1. 𝒑 𝒙 = 𝒂 𝒏 𝒙 𝒏
+ 𝒂 𝒏−𝟏 𝒙 𝒏−𝟏
+ + 𝒂 𝒏−𝟐 𝒙 𝒏−𝟐
+
…. + 𝒂 𝟏 𝒙 + 𝒂 𝟎
𝑷𝒐𝒍𝒚𝒏𝒐𝒎𝒊𝒂𝒍 𝒇𝒖𝒏𝒄𝒕𝒊𝒐𝒏 𝒑 𝒐𝒇 𝒅𝒆𝒈𝒓𝒆𝒆 𝒏
coefficient term
degree
constant term

2. 𝒑 𝒙 = 𝟓𝒕 𝟓
− 𝟐𝒕 𝟑
+ 𝟕𝒕

3. CHAPTER 2
Rational Functions

4. Lesson 1
Representing Real-Life
Situations Using Rational
Function

5. A. The local barangay received a budget of ₱100,000 to
provide medical checkups for the children in the
barangay. The amount is to be allotted equally among all
the children in the barangay. Write an equation
representing the relationship of the allotted amount per
child (y-variable) versus the total number of children (x-
variable).
𝑦 =
100,000
𝑥

6. 𝒚 =
𝟏𝟎𝟎,𝟎𝟎𝟎
𝒙
=
𝟏𝟎𝟎,𝟎𝟎𝟎
𝟏𝟎
= 10,000
No. of
children,
x
10 20 50 100 200 300 500 1000
Allocated
amount,
y
10,000 5,000 2,000 1,000 500 333.33 200 100

7. B. A philanthropist wants to
supplement the budget allotted for each
child by providing an additional ₱750
for each child in barangay. If g(x)
represents this new amount allotted for
each child, contruct a function
representing this relationship.
g 𝑥 =
100,000
𝑥
+ 750

8. 𝐠 𝒙 =
𝟏𝟎𝟎,𝟎𝟎𝟎
𝒙
+ 𝟕𝟓𝟎
No. of
children,
x
10 20 50 100 200 300 500 1000
Allocated
amount,
y
10,750 5,750 2, 750 1,750 1,250 1,083.33 950 850

9. Rational Function?
is a function of the form 𝒇 𝒙 =
𝒑(𝒙)
𝒒(𝒙)
where 𝒑(𝒙) and 𝒒(𝒙) are polynomial
functions, and 𝒒(𝒙) is not the zero
function.
What is

10. Example:
Suppose that 𝑐 𝑡 =
5𝑡
𝑡2+1
(in mg/mL) represents the
concentration of a drug in a patient’s bloodstream 𝑡
hours after the drug was administered. Construct a table
of values for 𝑐 𝑡 for 𝑡 = 1, 2, 5, 10. Round off answers
to three decimal places. Use the table to sketch a graph
and interpret the results.
𝑐 1 =
5𝑡
𝑡2+1
=
5(1)
(1)2+1
=
5
1+1
=
5
2
= 2.5
t 0 1 2 5 10
c(t) 2.5 2 0.962 0.4950

11. t 0 1 2 5 10
c(t) 2.5 2 0.962 0.4950

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