3.1 Distinguishing rational Function, Rational Equation and Rational Inequalities.pptx

3.1 Distinguishing rational Function, Rational Equation and Rational Inequalities.

1. Distinguishing Rational Function, Rational Equation and Rational Inequality SHS General Mathematics REYNALYN N. NACIONAL Special Science Teacher I

2. LEARNING OBJECTIVES: At the end of the lesson, the learner is expected to: Define rational function, rational equation and rational inequality distinguish rational function, rational equation and rational inequality . (M11GM – Ib – 2).

3. ADMISSION CARD Listed below are the skills and competencies you should possess before proceeding to this lesson. Read the statements and assess yourself about your level of understanding by answering YES if you agree and NO if otherwise. Statement Yes No 1. I can describe a rational expression     2. I can distinguish whether an expression is rational or not    

4. RATIONAL EXPRESSION A rational expression is an expression that can be written as a ratio of two polynomials in the form where and are polynomials and .  

5. RATIONAL EXPRESSION A rational expression can be described as a function where either the numerator and denominator, or both have a variable in it .

6. RATIONAL EXPRESSION EXAMPLES:  

7. RATIONAL EXPRESSION EXAMPLES:  

8. RATIONAL EXPRESSION EXAMPLES:  

9. RATIONAL EXPRESSION EXAMPLES:  

10. RATIONAL EXPRESSION NON-EXAMPLES:  

11. RATIONAL EXPRESSION Identify the following algebraic expression if they are rational or not.   Rational Expression because it is a ratio of two polynomials

12. RATIONAL EXPRESSION   Rational Expression because the numerator 5 is a polynomial (degree of 0)

13. RATIONAL EXPRESSION   Rational Expression because it is also a ratio of two polynomial

14. RATIONAL EXPRESSION   Not a Rational Expression since the numerator is not a polynomial

15. RATIONAL EXPRESSION   Not a Rational Expression since the numerator is not a polynomial

16. RATIONAL EXPRESSION   The expression is equal to ; so it is a rational expression  

17. WANTED!!! Call for Applicants for Contract of Service Workers For the purpose of 2023 census of population and housing, Philippine Statistics Authority is hiring enumerators. Any male or female Age - at least 18 years old and at most 45 years old Educational Attainment – at least SHS graduate Salary - ₱700.00 per day Physically fit for field work Interested applicants must submit application letter and Personal Data Sheet (PDS) to PSA- Quezon

18. QUESTIONS 1. What is the advertisement all about? 2. What job is offered by PSA? 3. Who can apply for the position? 4. How will you translate the required age mathematically?

19. QUESTIONS 5. Represent the salary (S) that will be received as a function of number of days used for work (n). 6. What are the mathematical symbols that you used in answering questions numbers 4 and 5? 7. Do you think the age requirement for the job is fair enough or is there a bias? Why do you say so? 8. Why do you think having a census is important?

20. Answers 1. The advertisement is a call for applicants for contract service workers to be hired as enumerators for the 2023 Census of Population and Housing by the Philippine Statistics Authority (PSA). 2. The PSA is offering the job of enumerators . 3. Male or female Age: at least 18 years old and at most 45 years old At least Senior High School (SHS) graduate Physically fit for field work

21. RATIONAL EQUATION RATIONAL INEQUALITY RATIONAL FUNCTION DEFINITION An equation involving rational expressions An inequality involving rational expressions A function of the form where and are polynomials and is not equal to 0 (i.e., EXAMPLE Extra Hints If it involves rational expression/s, only one variable and an equal sign (=) If it involves rational expression/s, only one variable x and have one of the inequality symbols If it involves rational expression/s, only one variable x and f(x) or y and have an equal sign (=) RATIONAL EQUATION RATIONAL INEQUALITY RATIONAL FUNCTION DEFINITION An equation involving rational expressions An inequality involving rational expressions EXAMPLE Extra Hints If it involves rational expression/s, only one variable and an equal sign (=) If it involves rational expression/s, only one variable x and f(x) or y and have an equal sign (=)

22. RATIONAL EQUATION An equation involving rational expression. Another way to identify a rational equation, if it involves rational expression/s, only one variable and an equal sign.

23. RATIONAL EQUATION EXAMPLE:  

24. RATIONAL EQUATION EXAMPLE:  

25. RATIONAL INEQUALITY An inequality involving rational expressions. EXAMPLE:  

26. EXAMPLE:  

27. RATIONAL FUNCTION A function of the form , where p(x) and q(x) are polynomial functions and q(x) is not equal to zero, q(x) . EXAMPLE:  

28. RATIONAL FUNCTION EXAMPLE:  

29. LET’S DISTINGUISH! Determine whether the given is a rational function, a rational equation, a rational inequality or none of these. Rational Inequality  

30. 2. Rational Equation  

31. 3. Rational Function  

32. 4. None of these  

33. 5. Rational Inequality  

34. How do we distinguish rational equations, rational inequality and rational function?

35. RATIONAL EQUATION RATIONAL INEQUALITY RATIONAL FUNCTION DEFINITION EXAMPLE Extra Hints

36. RATIONAL EQUATION RATIONAL INEQUALITY RATIONAL FUNCTION DEFINITION An equation involving rational expressions An inequality involving rational expressions A function of the form where and are polynomials and is not equal to 0 (i.e., EXAMPLE Extra Hints If it involves rational expression/s, only one variable and an equal sign (=) If it involves rational expression/s, only one variable x and have one of the inequality symbols If it involves rational expression/s, only one variable x and f(x) or y and have an equal sign (=) RATIONAL EQUATION RATIONAL INEQUALITY RATIONAL FUNCTION DEFINITION An equation involving rational expressions An inequality involving rational expressions EXAMPLE Extra Hints If it involves rational expression/s, only one variable and an equal sign (=) If it involves rational expression/s, only one variable x and f(x) or y and have an equal sign (=)

37. Any questions and clarifications regarding our lesson?

38. Activity No. __ Distinguishing Rational Equation, Rational Inequality and Rational Function A. Determine whether the given is a rational equation, rational function, a rational inequality, or none of these.   5.   6 .  

39. 7. 8. 9. 10 .