GENERAL MATHEMATICS FUNCTIONS VERSUS RELATIONS

Functions

1. GENERAL MATHEMATICS WEEK 1 1ST QUARTER BY NOENIE N. EMBAJADOR

2. FUNCTIONS AND THEIR GRAPHS

3. EROINTALPSHI What word can you see?

4. OVERVIEW Mathematics of long ago has observed several real-life situations wherein two or more quantities are related to each other. To better understand this relationship, functions were used as mathematical models. These are abstract models that use mathematical language to describe relationships.

5. STUDENT LEARNING OUTCOMES At the end of this chapter, you are expected to... Evaluate functions using the given value of the variable, solve problems that are represented by functions, and accurately construct mathematical models to represent real-life situations using functions.

6. PRETEST

7. Multiple Choice: Read each statement carefully. Choose the answer that is best described by the statement. Write the letter corresponding to your answer on a separate sheet of paper. Write x if the answer is not among the choices given. A For numbers 1 to 2, simplify the given expressions. 1. 5x 2 + 7x - 2x 2 - 10x + 5 a. 3x 2 - 3x + 5 c. 3x 2 - 3x + 5 b. 3x 2 + 2x + 5 d. 2x 2 + 3x + 5 2. 7 + 3x 2 - 5x 3 + 6x 2 - 2x a. 7 - 5x 3 + 3x 2 - 2x c. 7 + 5x 3 + 3x 2 - 2x b. 7 - 5x 3 + 9x 2 - 2x d. 7 + 5x 3 + 9x 2 - 2x

8. For numbers 3 to 5, determine the degree of each expression. 3. 5x 2 + 7x - 2x 2 - 10x + 5 a. 0 b. 1 c. 2 d. 3 4. 7 + 3x 2 - 5x 3 + 6x 2 - 2x a. 0 b. 1 c. 2 d. 3 5. 3x 2 y + 4xy 2 - 6x 2 y + 7y a. 0 b. 1 c. 2 d. 3

9. LOOK BACK

10. CHAPTER 1 KEY CONCEPTS OF FUNCTIONS: MATHEMATICAL MODELING USNG FUNCTIONS

11. Just Take the Jeepney! Maria rides a jeepney going to the market which is 14 km away from her house. The fare rate for the jeepney ride is P9.00 for the first 4 km and an additional P1.40 for every kilometer or a fraction of it thereafter. Questions: What mathematical model can be drawn out from the given situation? How much will she pay when she reaches the market?

12. Concept Check: The problem above introduces us to the simulation of real-life situations using functions. Functions as mathematical models can be written in the form y. = f(x). As some of the ancient mathematicians discovered, for whatever acceptable value(s) of the independent variable x, a corresponding value of y is derived. In writing mathematical models, we need to take note of the details of a given situation and categorize some real-life situations of different families of functions that match them. such as linear function, quadratic function, or cubic function and other models including rational, exponential, and piecewise-defined functions.

13. Concept Check: Take note of how we categorize the families of functions. In linear function, we use the model guide of y=mx or y=mx + b. This would be used in explaining the phenomenon that has a constant rate of change either by increasing or decreasing trend. For quadratic models, we use y=x 2 with a parabolic graph. Some of its applications are in the area of plane figures and problems with falling objects. Cubic models, y=x 3 can be used also in quantifying the maximum problems on falling objects. Cubic models, y=x 3 can be used also in quantifying the maximum possible volume of a figure and situations that involve patterns like production of goods.

14. Concept Check: Other models of functions may be used also to examine the quantifiable phenomena. Such a model is a piece-wise function that is defined by different equations on different domains. A mathematical model is a function that represents relationships between two or more different quantities.

15. ACTIVITY NO. 1 LET’S CHECK YOUR UNDERSTANDING

16. 1. You have a summer job that pays P250 for 8 hours of work a day.. Beyond 8 hours, you are also paid 1.5 times your hourly rate. a. Write a function of your salary for 5 days without exceeding 8 hours a day. b. Write a function of your salary in a day if you work beyond 8 hours. 2. An internet cafe has a flat rate of P15 for the first hour of playing, surfing, and the like. An additional P5 is charged for every hour excess afterward. Construct a mathematical model of the charge C(x), where x represents the total number of hours of playing in the internet cafe.

17. THANK YOU! SHOULD YOU HAVE ANY QUESTIONS?