GENERAL MATHEMATICS First lesson for Grade-11. pptx

First lesson in general mathematics. Grade-11 subject

1. GENERAL MATHEMATICS ARNEL JR. A. MACUTAY, LPT

2. What we are about to learn.. Define functions and piece – wise functions Determine whether a relation is a function or not; Represent real – life situations using functions including piece – wise functions.

3. FUNCTIONS Give another real – life situations involving functions.

4. Functions A function is a relation in which each element of the domain is paired with exactly one element of the range. Another way of saying it is that there is only one output ( y ) with each input ( x ). Illustration of Functions: a. set of ordered pair b. mapping or arrow diagram C. graphing

5. Functions A function is a relation in which each element of the domain is paired with exactly one element of the range. Another way of saying it is that there is only one output ( y ) with each input ( x ). Illustration of Functions: a. set of ordered pair {(3,2), (4,0), (5,1), (2,3)} {(1,2), (0,3), (1,6), (5,4)} {(3,4), (3,0), (3,1), (3,3)} {(4,2), (3,2), (6,2), (5,2)} Function Not Function Not Function Function

6. Functions A function is a relation in which each element of the domain is paired with exactly one element of the range. Another way of saying it is that there is only one output ( y ) with each input ( x ). Illustration of Functions: a. set of ordered pair (x, y) x – First element DOMAIN Independent Variable y – Second element RANGE Dependent Variable

7. Activity #1 Find the domain and the range of the ff. set of ordered pair. Do this in a ¼ sheet of paper. {(1,2), (3,4), (5,6), (7,8)} {(1,28), (2,29), (3,30), (4,31)} {(3,a), (4,b), (5,c), (6,d), (7,e)} {(2,9), (3,9), (6,4)} {(3,2), (3,3), (3,4), (3,6)} ANSWER! x = (1,3,5,7) , y = (2,4,6,8) x = (1,2,3,4) , y = (28,29,30,31) 3. x = (3,4,5,6,7) , y = (a,b,c,d,e,) 4 . x = (2,3,6) , y = (9,4) 5. x = (3) , y = (2,3,4,6)

8. Illustration of Functions: b. Diagram

9. To determine if y is a function of x, solve for y in terms of x. x² – y = 4 x² – 4= y Evaluate: (1)² – 4= y, (2)² - 4 = y, (3)² - 4 = y, (4)² - 4 = y y = -3 y = 0 y = 5 y = 12 x = (1,2,3,4) y = (-3,0,5,12) Example 1.1.1 Determine if the given equation represents y as a function of x . x² – y = 4

10. Let’s try this! Let g(x) = x² – 5x + 2 Find the following. a.) g(-1) b.) g(s) c.) g(x - 1 )

11. Let’s try this! Let g(x) = x² – 5x + 2 g(-1) = (-1)² - = 1 + 5 + 2 = 8 b. g(s) = (s) ² – 5(s) + 2 =s ² – 5s + 2  

12. Let’s try this! Let g(x) = x² – 5x + 2 c. g(x-1) = (x-1) ² -5(x-1) + 2 = x ² – 2x + 1- 5x + 5 + 2 = x ² – 7x + 8

13. ACTIVITY #2 Evaluate the function at each specified value of the independent variable and simplify. g(x) = 5x -2 a. g(0) b. g(-2) c. g(x+1) 2. f(t) = -2t + 3 a. f(0) b. f (1) c. f( t + 1)

14. Exercise #1 Evaluate the function at each specified value of the independent variable and simplify. g(x) = 10x -5 a. g(10) b. g(-4) c. g(x+3) 2. f(s) = -2s + 20 a. f(-15) b. f (10) c. f( s -5)

15. PEMDAS(PARENTHESIS, EXPONENT, MULTIPLICATION, DIVISION, ADDITION, SUBTRACTION) (0)³ + 10 = 15(5)²-50 = 3. 2(10)+30(5)-100 = 4. 125+9(15 )+2(5)² - 2 = 5. 1(10)³+199+40(10)² - 8 =

16. Illustration of Functions: c. Graphing VERTICAL LINE TEST (PENCIL TEST) If any vertical line passes through more than one point of the graph, then that relation is not a function.

17. THANKYOU FOR YOUR ACTIVE LISTENING!