Genmath Solving Rational Functions genera math

Genmath Solving Rational Functions.pptx

1. Lesson 4 Solving Problems Involving Rational Functions

2. At the end of this lesson, the learner should be able to accurately write a rational function to represent a real-life situation; and accurately find the value of a rational function at a given value of .    

3. How will rational functions be used to model a real-life situation? How will the domain and range of a rational function be used in order to solve real-life problems? How will rational functions be evaluated at specified values of the variable?

4. For this lesson, we will discuss solving problems involving rational functions . Before we proceed, let us watch this video to investigate about fixed and variable costs. ( Click on the link below to watch the video.) Glamour. “ How a 24-Year-Old Making $75K in NYC Spends Her Money | Money Tours | Glamour”. Retrieved 10 April 2019 from https://www.youtube.com/watch?v=Hnrfv4nR-DM

5. How do you spend your money? How much can you control your expenses?

6. Do you think the woman in the video spends her money wisely? Which areas can she make adjustments to if she wants to save money? What is the difference between fixed and variable costs? How can we use rational functions to represent variable costs?

7. Rational function a function of the form , where and are both polynomials and   1 Example: The function is a rational function since both the numerator and denominator are polynomials, and the denominator is not equal to zero.  

8. Asymptote a line that a curve approaches, but does not intersect 2 Example: Consider the rational function . The vertical asymptote of is . If , the denominator will become 0. Thus, the graph will never intersect the line .    

9. Asymptote a line that a curve approaches, but does not intersect 2 Example: Consider the rational function . Meanwhile, the horizontal asymptote of is the line . As becomes larger, the value of smaller, eventually approaching .    

10. Domain of a function the set of all values of that have corresponding values of ; it contains all values that go into the function   3 Example: The domain of the rational function is the set of all real numbers such that . In symbols, .    

11. Example: The range of the rational function is the set of all real numbers such that . In symbols, .   Range of a function the set of all values of that can be obtained from the possible values of ; it contains all possible values of the function   4

12. Example 1 : A parking area has a fixed entrance fee of ₱50, plus ₱25 for each hour of stay. Represent the average cost per hour using a rational function.

13. Example 1 : A parking area has a fixed entrance fee of ₱50, plus ₱25 for each hour of stay. Represent the average cost per hour using a rational function. Solution : The average cost can be calculated by finding the sum of the fixed entrance fee and the variable cost, then dividing the sum by the number of hours of stay. If the fixed entrance fee is ₱50 and the variable cost is ₱25, then total cost after hours is .  

14. Example 1 : A parking area has a fixed entrance fee of ₱50, plus ₱25 for each hour of stay. Represent the average cost per hour using a rational function. Solution : The total cost after hours is . Dividing it by the total number of hours gives us the average cost per hour.   Thus, the function of average cost per hour is given by:  

15. Example 2 : A movie rental store charges an initial fee of ₱250, then ₱50 for each movie you rent. What is the average cost function and the average cost per movie if you rent 5 movies?

16. Example 2 : A movie rental store charges an initial fee of ₱250, then ₱50 for each movie you rent. What is the average cost function and the average cost per movie if you rent 5 movies? Solution : The average cost function can be expressed as the sum of the initial fee and the variable cost, divided by the number of movies rented. Let be the number of movies rented.  

17. Example 2 : A movie rental store charges an initial fee of ₱250, then ₱50 for each movie you rent. What is the average cost function and the average cost per movie if you rent 5 movies? Solution : Let be the number of movies rented. If the initial fee is ₱250 and the variable cost is ₱50, then the total cost after movies is  

18. Example 2 : A movie rental store charges an initial fee of ₱250, then ₱50 for each movie you rent. What is the average cost function and the average cost per movie if you rent 5 movies? Solution : The total cost after movies is Dividing it by the total number of movies gives us the average cost per movie.  

19. Example 2 : A movie rental store charges an initial fee of ₱250, then ₱50 for each movie you rent. What is the average cost function and the average cost per movie if you rent 5 movies? Solution :  Thus, the function of average cost per movie is given by:    

20. Example 2 : A movie rental store charges an initial fee of ₱250, then ₱50 for each movie you rent. What is the average cost function and the average cost per movie if you rent 5 movies? Solution :  To determine the average cost per movie if you rent 5 movies, substitute into the average cost function.  

21. Example 2 : A movie rental store charges an initial fee of ₱250, then ₱50 for each movie you rent. What is the average cost function and the average cost per movie if you rent 5 movies? Solution :    

22. Example 2 : A movie rental store charges an initial fee of ₱250, then ₱50 for each movie you rent. What is the average cost function and the average cost per movie if you rent 5 movies? Solution :   Therefore, the average cost for each of five movies is ₱100.  

23. Individual Practice: Christy charges a fixed registration fee of ₱150 for a piano lesson, plus ₱80 per session. Represent the average cost per session using a rational function. A beach resort charges ₱3 500 upon check-in, plus ₱800 daily. What is the average cost function and the average daily cost if you stay for 5 days?

24. Group Practice : To be done in 2 to 5 groups Rosie receives a fixed daily salary of ₱650 as a teaching assistant at a private high school. She also receives ₱50 for each hour of work. Represent the average salary per hour using a rational function. If Rosie works for 5 hours, what will be her average salary per hour?

25. Rational function a function of the form , where and are both polynomials and   1 Asymptote a line that a curve approaches, but does not intersect 2

26. Domain of a function the set of all values of that have corresponding values of ; it contains all values that go into the function   3 Range of a function the set of all values of that can be obtained from the possible values of ; it contains all possible values of the function   4

27. How can you describe and represent a situation using rational functions? What are the difficulties you encounter while solving problems involving rational functions? How did you overcome them? How to we check if a given value of a variable is a solution to a rational equation?