General Mathematics - Evaluating Functions

Functions

1. EXERCISE

2. 2n - 1     (n-       (30 – 4n) Let n = 12

3. 2n - 1     (n-       (30 – 4n) Let n = 15

4. EVALUATION OF FUNCTIONS

5. ACTIVITY Meet best friends Emily and Anton. They have formed a partnership. Anton, being creative one, makes costumes jewelry. Emily, being business-minded, markets the jewelry Anton makes . In a recent month, they spent P1,000 on raw materials to make 50 pieces of jewelry and sold each for P25.00. Assuming that they are not required to pay a sales tax, their net profit depends on the number of jewelry sold.

6. 1. The problem includes three constants: the fixed cost of the raw materials (P1,000), the selling price for each piece (P25.00), and the total number of jewelry pieces made (50 )

7. 2. Let us use n to represents the number of pieces of jewelry sold and P for the net profit in pesos . a. What should be greatest value of n? the greatest of value of P ? b. What should be the least value of n? the least value of P? (Hint: refer to the table in the next page)

8. 3. Some of the data for selling the costume jewelry are shown in the table below. Number of Pieces of Costume Jewelry Sold (n) Net Profit in Pesos (P) -1,000 10 -750 20 -500 25 -375 30 -250 45 125

9. 4. A function machine that clearly shows the input, the process and the output after selling the costume jewelry is given as follows.

10. 5. Use the function machine to write an equation that shows algebraically how to compute the net profit given the number of pieces of jewelry sold.  

11. 6. If there are 40 pieces of jewelry sold, how much should be the profit?

12. Questions: In the previous activity we could also replace P (n) with y or any variable you like, what does the notation y = P (n) means? How do you call possible values of n that would satisfy the equation y the function P (n)? How about the resulting values of y or P (n)? How do you solve the values of P (n) given n? (Hint: refer to the previous activity)

13. Example 1. If , evaluate each. a. b . c. d.   Solution: Substitution Property of Equality. Simplify = 12  

14. Example 2. The price function represent the price for which you can sell x printed T-shirts. What must be the price of the shirt for the first 3 entries in the table?   Target Number of Shirts (x) 500 900 1300 Price per T-shirt P(x) P540 P460 P380 1 700 P300

15. ASSESSMENT A. Directions. Evaluate each function at the indicated values of the independent variable and simplify the result. 1. a . b. c. 2. a . b. c.    

16. B. Answer the problems that follow. 1. The function A described by gives the area of equilateral triangle with side s . a. Find the area when a side measures 8 inches. b. Find the area when a side measures 16 cm. 2. The function C described by gives the Celsius temperature corresponding to the Fahrenheit temperature F. a. Find the Celsius temperature equivalent to . b. Find the Celsius temperature equivalent to .  

17. Assignment Direction: Answer the problem below. As the lightning strikes, the time between the flash that we see and the thunder that we hear depends on the distance that we are from where the lightning struck. A table for this function is shown below. Distance (in kilometers), d 1 2 3 4 5 Time (in seconds), t 3 6 9 12 15

18. Questions: 1. Write a formula for this function. 2. Graph the data in the table by letting the x-axis represents the distance and the y-axis represents the time. 3. Why does it seem reasonable that the graph of this function should go through the origin?

19. Prepared by : DAREL F. CLAVERIA