FUNCTION AND THE RELATIONSHIP BETWEEN TWO VARIABLES

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1. FUNCTION AND THE RELATIONSHIP BETWEEN TWO VARIABLES

2. State whether the following relations are functions. (1, 2), (3, 4), (5, 6), (7, 8) Function

3. State whether the following relations are functions. (3, 6), (2, 4), (3, 7), (-7, 9) Not a Function

4. State whether the following relations are functions. Not a Function

5. State whether the following relations are functions. Function

6. Which relation mapping represents a function? A B A

7. Which relation mapping represents a function? A B B

8. Which is function? A B A

9. Shunly wants to buy juice for his friends. The price for juice is 5 pesos and Shunly has 4 friends. If he will buy for them, how much will it cost? How many is Shunly’s friends? How much will Shunly pay? INPUT OUTPUT

10. Shunly wants to buy juice for his friends. The price for juice is 5 pesos and Shunly has 4 friends. If he will buy for them, how much will it cost? How many is Shunly’s friends? How much will Shunly pay? INPUT OUTPUT

11. Function Notation =x+2 =x+2 is another way to write y in an equation. is read allowed as " " y f(x) f(x) f of x Function Notation

12. ( , ) ( , ) ( , ) Input Output x y x f( ) x can be written with other variables to represent different equations g(x), h(t), k(y), etc. = +2 = +2 = +2 f( ) x x g( ) x x h( ) t t f(x) Function Notation Ex. Given = +2, find = +2 = x f( ) x 1 f( ) 1 f( ) 1 3 f( ) 1

13. Example Explanation using PE MD AS P (none) E (none) M/D (Multiply 3 times 2) A/S (Subtract 5 minus 6) Pro Tip: Use parenthesis when plugging in. =5 -3 evaluate =5 -3 =5 = g( ) x x g( ) 2 (2) g( ) 2 -1 -6

14. Example Explanation using PE MD AS P (none) E (none) M/D (Multiply 3 times -8) (Divide -24 by 4) A/S (Subtract -6 minus 3) (Add -9 plus 5) Pro Tip: M/D and A/S are completed from left right. = -3+5 find = -3+5 = -3+5 = -3+5 = +5= 3 4 -24 h( ) x x h( ) -8 h( ) -8 3 4 4 -6 -4 (-8) -9

15. Example Explanation using PE MD AS P (add 1 and 0.5) E (1.5 times 1.5 times 1.5) M/D (500 times 3.75) A/S (none) Pro Tip: Parenthesis in PEMDAS says to do what is inside parenthesis first. =500(1+0.5) find =500(1+0.5) =500( ) =500( ) = v( ) t t 3 v( ) v( ) 3 3 3 1.5 3.75 1687.5

16. Real World Example The height of the tallest roller coaster in the world is modeled by the equation = -34 +140t -10t , where gives the height of the riders after seconds. Find the height of the riders after seconds. 2 g( ) t g( ) t 7 2 = -34 +140 -10 = -34 +140 -10 = -34 + - = = - 490 g( ) t (7) (7) (7) (49) 980 490 946 456 t After seconds, the roller coaster is at a height of feet. 7 456

17. A -7 Now you try! g( x )=4+5 x h( y )=2 - y k( t )=( t -3) -6 2 find h( 9 ) B -4 C 12 D 49 Given:

18. A -7 Remember that y is multiplied times . Try again! It helps to use parenthesis when plugging in. Almost there... h( y )=2 - y find h(9) B -4 C 12 D 49 h( 9 )=2 - (9)

19. A -7 C 12 Remember that multiplication happens before subtraction. Try again! Multiply times 9 and subtract what you get from 2. Not quite... h( y )=2 - y find h(9) B -4 D 49 h( 9 )=2 - (9)

20. A -7 So close... find h(9) B -4 C 12 D 49 It looks like you may have plugged into the wrong equation! You were asked to find h(9), not g(9). Try again! h( y )=2 - y h( 9 )=2 - (9)

21. A -7 h( y )=2 - y find h(9) B -4 C 12 D 49 h( 9 )= 2 - (9) = 2 - 18 3 = 2 - 6 h( 9 )= -4 Correct!

22. A -2 g( x )=4+5 x h( y )=2 - y k( t )=( t -3) -6 2 find k(1) B -10 C 2 D 9 Given:

23. A -2 find k(1) B -10 C 2 D 9 k( t )=( t -3) -6 2 =(-2) -6 2 k( 1 )=( 1 -3) -6 2 Remember that (-2) = -2 times -2 Try again! 2

24. A -2 find k(1) B -10 C 2 D 9 k( t )=( t -3) -6 2 Remember to plug it into the right equation. You were asked for k(1), not g(1). Try again!

25. A -2 find k(1) B -10 C 2 D 9 k( t )=( t -3) -6 2 =(-2) -6 2 k( 1 )=( 1 -3) -6 2 =4-6 You were so close, but 4-6 would bring the answer into the negative. Try again!

26. A -2 k( 1 )=(-2) -6 k( 1 )=( 1 -3) -6 k( 1 )=4-6 k( 1 )= -2 find k(1) B -10 C 2 D 9 k( t )=( t -3) -6 2 2 2

27. A 6 g( x )=4+5 x h( y )=2 - y k( t )=( t -3) -6 2 find g(-3) B -19 C -27 D -11 Given:

28. A 6 So close... g( x )=4+5 x find g(-3) B -19 C -27 D -11 Remember to use parentheses when plugging in. Try again! g( -3 )=4+5 (-3)

29. C -27 A 6 Almost... g( x )=4+5 x find g(-3) B -19 D -11 g( -3 )=4+5 (-3) Multiplication comes before addition. Try again!

30. A 6 Not quite... g( x )=4+5 x find g(-3) B -19 C -27 D -11 g( -3 )=4+5 (-3) =4+ -15 Remember we start at 4 and go down by 15. Try again!

31. A 6 g( x )= 4+5 x find g(-3) B -19 C -27 D -11 g( -3 )= 4+5 (-3) = 4+ -15 = -11 Correct!

32. You've completed the Activity!