Relations and Functions Section 2.1 ©2012, dangjim@gmail.com 4/17/2019 7:07 PM 2.1: Relations and Functions

2.1: Relations and Functions Definitions Relation is a pairing of 2 items (like (x, y)) Domain is the X -values in a relation. Also known as INDEPENDENT Variable Range is the Y -values in a relation. Also known as DEPENDENT Variable “Y depends on X.” Function is a relation that for each domain element, there is only 1 range element. _X_ do not repeat. 4/17/2019 7:07 PM 2.1: Relations and Functions

x y D R I Think of: “A doctor needs his or her ID to eXamine you” 4/17/2019 7:07 PM 2.1: Relations and Functions

Example 1 The cost of a tank of gas depends on the number of gallons purchased. What is the input and output? Input: Number of Gallons Output: Cost of a tankful of gas 4/17/2019 7:07 PM 2.1: Relations and Functions

Output: Volume of a Cube 2.1: Relations and Functions Your Turn The volume of a cube depends on the length of its edges. What is the input and output? Input: Edge Length Output: Volume of a Cube 4/17/2019 7:07 PM 2.1: Relations and Functions

2.1: Relations and Functions Example 2 Identify the domain and range of this function: 4/17/2019 7:07 PM 2.1: Relations and Functions

2.1: Relations and Functions Example 3 Identify the domain and range of this function: 4 –5 9 –1 Input –2 7 Output 4/17/2019 7:07 PM 2.1: Relations and Functions

2.1: Relations and Functions Your Turn Identify the domain and range of this function: 4/17/2019 7:07 PM 2.1: Relations and Functions

Is a relation a function? What is a function? Can a function be a relation? Can a relation be a function? 4/17/2019 7:07 PM 2.1: Relations and Functions 9

2.1: Relations and Functions Example 4 Is this relation a function? 4/17/2019 7:07 PM 2.1: Relations and Functions

2.1: Relations and Functions Your Turn Is this relation a function? 4/17/2019 7:07 PM 2.1: Relations and Functions

2.1: Relations and Functions Boys vs. Girls Is this relation a function? a b c 1 2 3 Girls Boys a b c 1 2 3 Girls Boys 4/17/2019 7:07 PM 2.1: Relations and Functions

2.1: Relations and Functions Example 5 Which mapping is a function? Choice A: Choice B: 3 1 –1 2 2 –1 3 –2 4/17/2019 7:07 PM 2.1: Relations and Functions

2.1: Relations and Functions Your Turn Which mapping is a function? Choice A: Choice B: 4/17/2019 7:07 PM 2.1: Relations and Functions

2.1: Relations and Functions Vertical Line Test Vertical Line Test: a relation is a function if a vertical line drawn through its graph, passes through only one point. AKA: “The Pencil Test” Take a pencil and move it from left to right (–x to x); if it crosses more than one point, it is not a function 4/17/2019 7:07 PM 2.1: Relations and Functions

2.1: Relations and Functions Example 6 Would this graph be a function? 4/17/2019 7:07 PM 2.1: Relations and Functions

2.1: Relations and Functions Example 7 Would this graph be a function? 4/17/2019 7:07 PM 2.1: Relations and Functions

2.1: Relations and Functions Your Turn Would this graph be a function? 4/17/2019 7:07 PM 2.1: Relations and Functions

2.1: Relations and Functions Evaluating Functions Replace its variable with a given number or expression. Remember to think of the function machine; for every x, there is a y-coordinate 4/17/2019 7:07 PM 2.1: Relations and Functions

2.1: Relations and Functions Example 8 Given g(x) = x2 – 3, determine g(2). (2)2 g(2) = 4 – 3 g(2) = 1 4/17/2019 7:07 PM 2.1: Relations and Functions

2.1: Relations and Functions Example 9 Given f(x) = x2 – 2x + 4, evaluate f(–5). 4/17/2019 7:07 PM 2.1: Relations and Functions

2.1: Relations and Functions Your Turn Given f(x) = x2 – 6x + 9, evaluate f(1/2). 4/17/2019 7:07 PM 2.1: Relations and Functions

2.1: Relations and Functions Assignment Page 76 3-23 odd, 35-39 odd 4/17/2019 7:07 PM 2.1: Relations and Functions