This document provides definitions and examples of rational functions, rational equations, and rational inequalities. It begins with a "Two Pics One Word" activity to introduce the topic. It then defines each concept: rational functions are ratios of polynomials where the denominator is not zero, rational equations involve rational expressions set equal to each other, and rational inequalities involve rational expressions and inequality symbols. Examples of each are given. The document concludes with an exercise asking students to identify examples as rational functions, equations, or inequalities. The overall purpose is for students to understand the differences between these concepts and be able to identify examples of each.

1. GENERAL
MATHEMATICS
Merianne Mae C.
Alingalan

2. TITLE: “TWO PICS ONE WORD”
“Guess the word”
1. N A I O L T R A
2. L Q U A I E N S I E T I
3. I N O T F U N C
4. U A Q E O I N T
5. R E S P E X N I O S S
RATIONAL
INEQUALITY
FUNCTION
EQUATION
EXPRESSION

3. Rational Functions, Equations
and Inequalities

4. At the end of the lesson, the students will be able to:
• identify the difference between rational function,
equation, and inequality;
• create an example of rational function, equation
and inequality; and
• initiate the rational functions by representing real-
life problems.

5. Rational expression
• can be written as a ratio of two polynomials.
• in the form
𝐴
𝐵
where A and B are polynomials and B ≠ 0.
• are also called algebraic fractions.
The following are rational expressions:
7
𝑎𝑏
,
𝑥2 − 𝑥 − 6
𝑥 + 2
, 𝑎𝑛𝑑
𝑥2 + 7𝑥 + 10
𝑥 + 5
The following are not rational expressions:
5 + √𝑥
𝑥
,
𝑥2
1
+ 2
𝑥 + 2
, 𝑎𝑛𝑑
𝑥2
3
+ 4
𝑥 − 1

6. Rational Equation
An equation involving rational
expressions.
𝟐
𝒙
−
𝟑
𝟐𝒙
=
𝟏
𝟓
𝟓
𝒙
−
𝟏
𝟑
=
𝟏
𝒙

7. Rational Inequality
An inequality involving rational
expressions.
𝟓
𝒙 − 𝟑
≤
𝟐
𝒙
𝟔
𝒙 − 𝟐
≥ −𝟒

8. Rational Function
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 (i.e., q(x) ≡ 0).
f (x) =
𝒙𝟐+𝟐𝒙+𝟑
𝒙+𝟏
𝒇 𝒙 =
𝒙𝟐
+ 𝟏
𝒙 − 𝟐

9. LET’S HAVE SOME
EXERCISES!

10. Direction: Determine whether the given is a rational function, a
rational equation, a rational inequality or none of these.
Rational Equation
None of these
Rational Function
Rational Inequality
Rational Equation
1.
𝟐+𝒙
𝒙−𝟏
= 8
2. 𝒙 > 𝒙 + 𝟐
3. f(x) = 6 -
𝒙+𝟑
𝒙𝟐−𝟓
4. 2x ≥
𝟕
𝒙+𝟒
5.
𝒙
𝟐
=
𝟒
𝒙+𝟗𝒙𝟑

11. “The only way to learn mathematics is to do
mathematics.”
— Paul Halmos
THANK YOU!