advertisement

Algebra II 2-1 Part One: Relations and Functions Objectives: To graph relations; to identify functions Warm Up: Graph the points on the coordinate plane. 1) {(−2, 4), (3, −2), (−1, 0), (1, 5)} 2) {(−2, 1), (−1, 0), (0, 1), (1, 2)} A relation is a set of pairs of input and output values. You can represent a relation in four different ways as shown below. Ordered Pairs (𝑥, 𝑦) Mapping Diagram Table of Values (−3,4) x (3, −1) (4, −1) (4,3) Graph The domain of a relation is the set of inputs, also called x-coordinates, of the ordered pairs. The range is the set of outputs, also called y-coordinates, of the ordered pairs. Example 1) Make a mapping diagram of each of the relations. Identify the domain and range. a) {(−1, −2), (3,6), (−5, −10), (3,3)} b) {(2,8), (−1,5), (0,8), (−1,3), (−2,3)} Quick Check: Make a mapping diagram of each of the relations. Identify the domain and range. 1) {(0,1), (1,2), (3,5), (4,8), (6,9)} 2) {(−3,12), (0,9), (2,7), (4,3), (9, −2)} A function is a relation in which each element of the domain corresponds to exactly one element of the range. Example 2) Does the mapping diagram represent a function? Explain. c) d) Quick Check: Is the relation a function? Explain. 3) 4) -3 -2 0 1 4 7 1 4 6 8 -1 1 6 You can use the vertical line test to determine whether a relation is a function. The vertical line test states that if any vertical line passes through more than one point on the graph of a relation, then the relation is not a function. If a vertical line passes through a graph at more than one point, there is more than one value in the range that corresponds to a value in the domain. Example 3) Use the vertical line test to determine if the relation is a function. Explain. e) f) Quick Check: Use the vertical line test to determine if the relation is a function. Explain. 5) 6)