- EXERCISE 1C.1: FUNCTION Direction: Answer the following problems below. Write your solution in short/long coupon bond and send your output (photo of your answer) in google classroom. 1. Which of the following relations are functions from A to B? a. {(1, -2), (3, 7), (4, -6), (8, 11)} A= {1, 3, 4, 8}, B= {-2, 7,-6, 11} b. {(1, 0), (1, -1), (2, 3), (4, 10)} A = {1, 2, 4}, B= {1, 0, -1, 3, 10} c. {(a, 2), (b, 3), (c, 2), (d, 3)} A= {a, b, c, d}, B= (2, 3} d. {(1, 1), (1, 2), (2, 3), (-3, 4)} A= (1, 2, -3}, B= {1, 2, 3, 4) e. {(1,1), (-1, 1), (2, 4), (-2, 4)} A= (0, 1, -1, 2, -2}. B = (1, 4 ) I1. Which of the following relations represent a function? 2. 3. 35 | Page 4. 5 . Ill. 1. If f (x) = 2x + 1, find the range when domain = {-3, -2, -1, 0, 1, 2, 3} 2. If f (x) = x+3,0s xs 4, find its range. 3. If f (x) = x2, -3 5 x s 3, find its range.- CONTENT EXPLORATION: FUNCTION A function is a relation in which each x-element has only y-element associated with it. Given a set of set or ordered pairs, a relation is a function if there are no repeated x-value. In the figure above, we can see the ordered pairs (1, a), (2, b), (3, c), (4, d) have the unique element of x with respect to y. Therefore, set A with respect to set B is function. Examples: 1. Write the domain and range of the following sets and tell whether if it is a function or not function. If it is not a function, justify your answer. 1. {(1, -2), (3, 7), (4, -6), (8, 1)} A= {1, 3, 4, 8 } B = {-2, 7, -6, 1, 2} 2. {(1, 0), (1, -1), (2, 3), (4, 10)} A = (1, 2, 4} B= {0, -1, 3, 10} 3. {(a, b), (b, c), (c, b), (d, c)} A= {a, b, c, d, e} B = {b, c} 4. {(2, 4), (3, 9), (4, 16), (5, 25)} A= {2, 3, 4, 5 } B = {4, 9, 16, 25} 5. {(1, -1), (2, -2), (3, -3), (4, -4) } A= {0, 1, 2, 3, 4 ) B= {-1, -2, -3, -4, -5} 31 | Page Answers: 1. It is a function. Domain = {1, 3, 4, 8} Range = {-2, 7, -6, 1} 2. It is not a function, because 1st two ordered pairs have the same first elements. 3. It is not a function. Domain = {a, b, c, d) is not equal to A, Range = {b, c} . It is a function. Domain = (1, 2, 3, 4} Range = {-1, -2, -3, -4} 5. It is not a function. Domain = {1, 2, 3, 4) is not equal to A Range = (1, -2, -3, -4, -5} Remember! In a function, no two ordered pairs have the same first element". "Hindi pwedeng parehas kayo ng "X", it is not a function" 11. State whether each of the following relations represent a function or not. 1. 2.3. 4 Solution: 1. Diagram 1 is not a function because the element b of A doesn't have an image in B. 2. Diagram 2 is not a function because the element c of A doesn't have a unique image in B. 3. Diagram 3 is a function because every element of A has a unique image in B. 4. Diagram 4 is a function because every element in A has a unique image in B. Ill. Which of the following relations from R -> Rare functions? 1. y = 3x + 2 2. y