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Lesson 3.1 Objectives: Vocabulary: EQ: What is a function? Identifying functions, Finding Domain and Range and identifying independent and dependent variables. 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. y=x+5 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 x output y 0 5 1 6 2 7 3 8 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. Decide if the following tables represent a function input output input output 1 2 3 4 5 8 11 14 1 2 2 3 4 5 6 7 Yes a function Not a function input 1 2 3 4 output 5 5 5 5 Yes a function 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 Determine the range of y = 2x +5 when the domain is 0, 1, 2, 3 and 4 Domain Range 0 1 2 3 4 Range is 5, 7, 9, 11and 13 Find the domain and the range of the function Domain: Continuous change in x Range: Continuous change in y -2 < x < 3 -1 < y < 2 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