The document discusses rational functions, expressions, equations, and inequalities. It defines a rational expression as a ratio of two polynomials. Examples of rational expressions, equations, and inequalities are provided. The learning outcomes are to distinguish between rational functions, expressions, equations, and inequalities, and to represent real-life situations using rational functions. The document contains questions to identify whether examples given are rational expressions, equations, inequalities, or none of the above.

1. RATIONAL FUNCTIONS
EXPRESSIONS, EQUATIONS AND
INEQUALITIES
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General Mathematics

2. RATIONAL FUNCTIONS
› LEARNING OUTCOMES:
› Distinguish rational functions, rational
equations and rational inequalities.
› Represent real life situations using rational
functions.

3. RATIONAL EXPRESSION
› A rational expression is an expression that
can be written as a ratio of two
polynomials.
Identify if they are rational or not.
( ) yes ( ) no

4. RATIONAL EXPRESSION
› A rational expression is an expression that
can be written as a ratio of two
polynomials.
Identify if they are rational or not.
( ) yes ( ) no

5. RATIONAL EXPRESSION
Identify if they are rational or not.
( ) yes ( ) no
( ) yes ( ) no
( ) yes ( ) no
( ) yes ( ) no

6. RATIONAL EXPRESSION
Identify if they are rational or not.
( ) yes ( ) no
( ) yes ( ) no
( ) yes ( ) no
( ) yes ( ) no

7. RATIONAL EXPRESSION
Identify if they are rational or not.
( ) yes ( ) no
( ) yes ( ) no
( ) yes ( ) no
( ) yes ( ) no

8. RATIONAL EXPRESSION
Identify if they are rational or not.
( ) yes ( ) no
( ) yes ( ) no
( ) yes ( ) no
( ) yes ( ) no

9. RATIONAL EXPRESSION
Identify if they are rational or not.
( ) yes ( ) no
( ) yes ( ) no
( ) yes ( ) no
( ) yes ( ) no

10. RATIONAL EQUATION
An equation involving rational expressions.
Example:
𝟐
𝒙
−
𝟑
𝟐𝒙
=
𝟏
𝟓

11. RATIONAL INEQUALITY
An inequality involving rational expressions.
Example:
𝟓
𝒙−𝟑
≤
𝟐
𝒙

12. RATIONAL FUNCTION
A function of the form of 𝒇 𝒙 =
𝒑(𝒙)
𝒒(𝒙)
where
𝒑(𝒙) and 𝒒(𝒙) are polynomials, and 𝒒(𝒙) is
not the zero functions.
Example: 𝒇(𝒙) =
𝒙 𝟐+𝟐𝒙+𝟑
𝒙+𝟏
or 𝒚 =
𝒙 𝟐+𝟐𝒙+𝟑
𝒙+𝟏

13. Determine whether the given is a rational
function, a rational expression, a rational
equation, a rational inequality, or none of these.
(a) 𝑦 = 5𝑥3
− 2𝑥 + 1 (e) 6x −
5
𝑥+3
≥ 0
(a)
8
𝑥
− 8 =
𝑥
2𝑥−1
(f)
5−𝑥3
𝑥
(b) 𝑥 − 2 = 4 (g)
𝑥−1
𝑥+1
= 𝑥3
(d) 5x4 - 6x7 + 1 (h) 𝑦 =
7𝑥3−4 𝑥+1
𝑥2+3

14. THANK YOU
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