A jeepney ride costs P 7 00 for

A jeepney ride costs P 7. 00 for the first 4 kilometers, and each additional integer kilometer adds P 1. 50 to the fare. If you were to ride a jeepney, how much will you pay a. going to school which is 3 kms. away? P 7. 00 b. going to the mall which is 8 kms. away? P 13. 00 1

Functions as representations of real-life situations 1. Given a function C, represent the cost of buying x meals if one meal costs P 40. 2. A buko pie store can produce buko pie at P 95. it is estimated that if the selling price of the buko pie is x pesos, then the number of buko pie sold each day is 1000 – x. a. Express the daily profit of the store as a function of x. b. Determine the daily profit given that the selling price is P 160. 2

Functions as representations of real-life situations 3. A rectangular field is to be enclosed with 240 m of fence. Let x be the length of the field. Express the area of the field as a function of x. 4. A cylindrical can is to have a capacity (volume) of 24 cubic inches. The cost of the material used for the top and bottom of the can is ₱ 15 per square inch, and the cost of the material used for the curved side is ₱ 9 cents per square inch. Express the cost of constructing the can as a function of its radius. 3

Piecewise-defined functions Functions are often defined using more than one formula, where each individual formula describes the function on a subset of the domain. A function defined in this way is sometimes called a piecewise-defined function. 4

Represents real life situations using functions 1. A jeepney ride costs P 8. 00 for the first 4 kilometers, and each additional integer kilometer adds P 1. 50 to the fare. Use a piecewise function to represent the jeepney fare in terms of the distance d in kilometers. a. going to school which is 3 kms. away? b. going to the mall which is 8 kms. away? 5

Piecewise-defined function n 6

Piecewise-defined function How much is the cost of producing a. 5000 copies? b. 40000 copies? 7

Represents real life situations using functions 3. A user is charged P 300 monthly for a particular mobile plan, which includes 100 free text messages. Messages in excess of 100 are charged P 1 each. Represent the amount a consumer pays each month as a function of the number of messages m sent in a month. a. How much will she be charged if she sends 50 text messages? b. How much will she be charged if she sends 175 text messages? 8

Algebraic Functions Two main types of functions: Algebraic functions – those functions that can be obtained by a finite combination of constants and variables together with the four basic operations, exponentiation, or root extractions. Transcendental functions – those that are not algebraic. (usually involving exponentials, logarithms, circular and inverse circular functions). 9

BASIC Operations ON FUNCTIONS Let f and g be functions of the variable x. n Sum n Difference n Product n Quotient 10

BASIC Operations ON FUNCTIONS Let f and g be functions of the variable x. n Composite f –g 11

OPERATIONS ON FUNCTIONS Examples: 1. Given and find the sum, difference, product, and quotient of and their corresponding domain. , Clearly, 12

OPERATIONS ON FUNCTIONS Given and Clearly, 13

OPERATIONS ON FUNCTIONS Given and Clearly, 14

OPERATIONS ON FUNCTIONS Given and 15

OPERATIONS ON FUNCTIONS Given and . 16

OPERATIONS ON FUNCTIONS Given and 17

Example 2. Let (x) = x 2 + 1 and g(x) = 3 x + 5. Find the following: a. Since (1) = 2 and g(1) = 8, use the definition to get 18

Example Let (x) = x 2 + 1 and g(x) = 3 x + 5. b. Since (– 3) = 10 and g(– 3) = – 4, use the definition to get 19

Example Let (x) = x 2 + 1 and g(x) = 3 x + 5. c. Since (5) = 26 and g(5) = 20, use the definition to get 20

Example Let (x) = x 2 + 1 and g(x) = 3 x + 5. d. Since (0) = 1 and g(0) = 5, use the definition to get 21

Example 3. Let (x) = 2 x 2 – 3 x. Find the difference quotient and simplify the expression. Caution Notice that (x + h) is not the same as (x) + (h). 22

Example 4. Let (x) = 2 x – 1 and g(x) First find g(2). Now find 23

Example 24

TIME TO THINK n