1. Objectives:Identifying functions, Finding Domain and Range and identifying independent and dependent variables. Vocabulary: Function – is a rule or math problem that shows a relationship between two quantities. Input – is the independent variable also called the domain. The input is the x –value. Output – is a dependent variable and the solution to the function and is also called the range. The range is the y-value. Example: A sample Input Output table: The first (left) column is the input (domain) Independent variable. The second (right) column is the output (range) Dependent variable. Input xoutput y 0 1 2 3 y = x + 5 Lesson 3.1 EQ: What is a function? 5 6 7 8

2. Functions: For a function to exist, it must be true that for each input there is exactly one output. (The input (x) does not repeat) Examples: a) Student ID #’s do not repeat. No students have the same ID#. b) Phone numbers do not repeat. Two different homes do not have the same number. inputoutput 1 5 2 8 3 11 4 14 Decide if the following tables represent a function Yes a function inputoutput 1 4 2 5 2 6 3 7 Not a function input output 1 5 2 5 3 5 4 5 Yes a function

3. Relation – a rule that associates more than one output with an input. A relation is defined to be any set of ordered pairs. Vertical Line Test A relation is a function if and only if no vertical line passes through two or more points on the graph. Function Not a Function Function Not a Function. A vertical line can be drawn through two points

4. Determine the range of y = 2x +5 when the domain is 0, 1, 2, 3 and 4 DomainRange 0 1 2 3 4 Range is 5, 7, 9, 11and 13

5. Find the domain and the range of the function Domain: Continuous change in x -2 < x < 3 Range: Continuous change in y -1 < y < 2

6. The dependent variable depends on the value of the independent variable. When an equation represents a function, the dependent variable is defined in terms of the independent variable. The statement “y is a function of x” means that y varies depending on the value of x. The function y = −3x + 12 represents the amount y (in fluid ounces) of juice remaining in a bottle after you take x gulps. y is dependent variable. It depends on x (independent variable) Fluid remaining # of gulps