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Algebra 2 – Relations and Functions Name __________________________ I. What is a function? Definition: __________________________________________________________________________________ Draw a representation of a “function machine” here: When y is a function of x, this means ___________________________________________________ 2. Function vocabulary: Domain: _____________________________________________ Range: ______________________________________________ Remember! If a relation is a function there cannot be more than _______ possible output value for each _______________ value. 3. Using a verbal description to identify a function a. Consider the relationship of CHS student ID numbers and student locker numbers. Write “ID #” in the input box and “locker number” in the output box. Is a student’s locker number a function of their ID number? Why or why not? Complete the boxes below: 4. Which of the following tables represents a function? Explain your answer. Input Out put -3 2 5 1 5 8 7 15 Input Output -3 5 6 7 2 2 2 2 5. Evaluating Functions f ( x) reads _________________ f is _______________________ ( x) in the parentheses means ______________________________________ For example... If g ( x) 2 x 5 then g (3) 11 , where is ___________________________________ is ___________________________________ and 11 is __________________________________ (why?) You try it! If f ( x) 5 3 x evaluate: a) f (3) b) f (2) c) f ( A) f (3) 4 f ( 2) 11 f ( A) 5 3 A Example 1: State the domain and range of the relation. Determine if the relation is a function. 6,1, (5,9), (3,7), (1,7), (6,9) You Try: State the domain and range of the relation. Determine if the relation is a function. x y 2 -2 -1 -1 -2 0 -1 1 2 2 A relation in which the domain is a set of individual points, like the relation in the graph below is said to be a discrete relation. Notice that its graph consists of points that are not connected. y=#of runs X=innings When the domain of a relation has an infinite number of elements and the relation can be drawn with a line or smooth curve, the relation is a continuous relation. When using the graph of a relation (both discrete and continuous, you can use the vertical line test to determine if a relation represented by the graph is a function. If a vertical line can be drawn that hits the graph at more than one point = NOT a function. If a vertical line can be drawn that hits the graph at only one point = Is a function. EX: Determine if the relation is a function.