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Acc. Coordinate Algebra: Unit 3 Name___________________ Date_________________ Period________ Lesson 1: Identifying and Evaluating Functions Guided Notes Standard and Skills F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y=f(x). F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. SWBAT identify whether a relation is a function by looking at a graph, table of values, or an equation. SWBAT use function notation to evaluate the output of a function given a particular input. SWBAT identify the domain and range for a set of values. Part I: Identifying Functions Important Vocabulary Relation: Any set of ____________________ that has an ______________________. Function: A _____________________ such that every single _______________ has exactly _________________ output. Input (x-coordinates): also called the __________________. Output (y-coordinates): also called the ________________. How to Determine if a Relation is a Function: 1. If we are looking at a table of values, each input must have ______________________ output. 2. If we are looking at the graph….we must use the vertical line test: No vertical line can pass through _______________________________________ points on the graph. Example 1: Does the relationship represent a function? Function: y x 6 x (input) -3 0 7 8 y (output) -9 -6 1 2 Example 2: Does the relationship represent a function? Example 3: Does the relationship represent a function? y = 3x x=3 y =3 Guided Practice Are these relations functions? Give an explanation on the right hand side. 1. 3,2 , 4,3 , 5,4 , 6,5 2. 2. 3. 3. 4. Table of Values 5. input 3 2 0 3 output 4 -1 2 -3 Independent Practice Explain whether the relation is a function or not. 1. 4. 2. Input 1 2 Output 7 -7 8 -8 5. 3. Input Output 3 5 7 2 4 6 6. Input 0 2 4 6 Output -6 -4 -2 0 Part II: Using Function Notation What is function notation? Function Notation is _________________________________________________. It is pronounced ________________________. f(x) is a fancy way of writing _____ in an _______________. Example 1: Evaluate f x x2 2x 3 , when x 3 and x 4 . Guided Practice Evaluate the function when x 3, x 0, and x 2 . 1. f x 2x 5 2. h x 6x 2 3. g x 2.4x Independent Practice Evaluate the function x 3, x 0, and x 2 . 1. f x 0.5x 12 2. h x 2 x 1 3 3. f x 3 x2 5 4. f(x) = x2 – 2x + 7 5. f(x) = 3x