A. Determine the function in the given ways to represent functions. Write FUNCTION if it is and NOT FUNCTION if it is not. 1. Set of Ordered Pairs a. {(2,5), (3,7), (4,9), (5,11), (6,13)} b. {(1,3), (2,4), (2,5), (3,6), (4,7)} 0- {(-3.1). (-1. 2). (1 3). (3.4). (5,5) 2. Table of Values A.X v 3.x v v 1-m- 3. Mapping Diagram A. B. C. I a ' 4. Graphs 4a 4 4: 5. Equations: Represent each situation with a function equation. a. Give a function C that can represent the cost of buying x meals, if one meal costs P4000. b. A person is earning P600.00 per day to do a certain job. Express the total salary S as a function of the number n of days that the person works. 0. Judy is earning P300.00 per day for cleaning the house of Mrs. Perez and additional P25.00 for an hour of taking care Mrs. Perez's child. Express the total salary S of Judy including the time t spent for taking care of the child. B. Represent the given situation with a piece-wise function. 1. 1. A taxi ride costs P4000 for the rst 1 kilometer and each additional kilometer (or a fraction thereof) adds P1000 to the fare. Use a piece-wise function to represent the taxi fare F in terms of the distance d in kilometers. 2. The fee to park in the parking lot of a shopping mall costs P4000 for the first 2 hours and an extra P1000 for each hour (or a fraction of it) after that. If you park more than 12 hours, you instead pay a flat rate of P200.00. Represent your parking fee using the function P(t) where t is the number of hours you parked in the mall. Evaluate the following functions to the specified value: 1. f(x) = 9x - 4; find f (4). 2. g(x) = -7x - 11; find g(-2). 3. h(x) = x2 - 7x - 13; find h(0). 4. s(t) = 6t - 7; find s(t - 2). 5. u(v) = 202 + 3v + 1; find u(w + 3) Guided examples 1. Given the function f(x) = 5x - 2, find f(3). Solution: Substitute 3 into the function in place of x. f(3) = 5(3) - 2 Perform the series of operations following the GEMDAS Rule. f(3) = 15 - 2 f(3) = 13 Therefore, the value of the function f(x) = 5x - 2 when x = 3 is 13. 2. Find the value of k(m) = 2m2 - 3m + 5 when m = -2. Solution: Substitute -2 into the function in place of m. h(-2) = 2(-2)2 -3(-2) +5 Perform the series of operation following the GEMDAS Rule. h (-2) = 2(4) -3(-2) +5 =8+6 +5 h(-2) = 19 Therefore, the value of the function h(m) = 2m - 3m + 5 when m = -2 is 19 3. Find t (3v) when t (x) = x2 - 2x + 1. Solution: When substituting expressions, like 3v, into a function, use parentheses to prevent algebraic errors. For this problem, we will use (3v). Replace all x's of the function with 3v. t(3v) = (3v)2 -2(3v) + 1 Perform multiplication of algebraic expressions. Apply Power of a Product Rule of Laws of Exponents in the first term. t(3v) = 9v2 -6v + 1 Therefore, the value of the function t (x) = x2 - 2x + 1 when x = 3v is 9v2 - 6v + 1. 4. Given g (x) = 2x2 + 4x - 3, find g (2a + 3). Solution: Be sure to use parentheses! Special product (square of a binomial) is involved 2a + 3 here. 2a+3 Substitute (2a + 3) into the function in place of x. g (x) = 2(2a + 3)2 + 4(2a + 3) - 3 6a+9 Simplify first (2a + 3)2 before applying the distributive property. 4a + 6a Rewrite the equation g (x) = 2(4a2 +12a +9) + 4(2a + 3) - 3 Apply the Distributive Property. g (x) = 8a2 + 24a + 18 + 8a + 12 - 3 4a +12a+9 Combine similar terms. g (x) = Baz + 32a + 27 Therefore, g(2a + 3) = 8a2 + 32a + 27