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Warm-up • • • • • • • • 1. Given this relation: {(2, -1), (4, -1), (3, 2), (5, 1), (4, 2), (5, 1)} Domain? Range? Function or Not? Explain why? 2. Convert these to Interval Notation x<6 2≤ x<5 Warm-up • • • • • 1. Given this relation: {(2, -1), (4, -1), (3, 2), (5, 1), (4, 2), (5, 2)} Domain? {2,3,4,5} Range? {-1,1,2} Function or Not? NO, duplicated “x” values • 2. • x < 6 in interval notation (-∞, 6) • 2 ≤ x < 5 in interval notation [2, 5) Continuous Functions vs Discrete Functions Domain and Range Chapter 2 Section 2-1 Pages 72-81 Objectives •I can determine Domain and Range from a Continuous Graph •I can identify a discrete and continuous function Important Vocabulary •Discrete Function •Continuous Function Discrete Function • A function with ordered pairs that are just points and not connected. Discrete Function Continuous Functions?? • A function is continuous if it has an infinite domain and forms a smooth line or curve • Simply put: It has NO BREAKS!!! • You should be able to trace it with your pencil from left to right without picking up your pencil 8 The domain of the function y = f (x) is the set of values of x for which a corresponding value of y exists. The range of the function y = f (x) is the set of values of y which correspond to the values of x in the domain. y Range x 4 -4 Domain Example: Find the domain and range of the function f (x) = x 3 from its graph. y Range (–3, 0) 1 –1 Domain The domain is [–3,∞). The range is [0,∞). x Example 1 Domain (, ) Range [3, ) Example 2 Domain (, ) Range (, 4] Example 3 Domain [0, ) Range (, ) 8 Domain 6 (, ) 4 Range 2 [2, ) -5 5 -2 Domain 6 4 (,3] Range [1, ) 2 -5 5 Domain (, ) Range [0, ) Domain [0, ) Range [0, ) Domain (, 1) U [1, 6] Range (, 6) Homework • WS 1-5: Domain and Range