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Function Notation Traditionally, functions are referred to by the letter name f, but f need not be the only letter used in function names. The following are but a few of the notations that may be used to name a function: f (x), g(x), h(a), A(t), ... Examples f ( x) x g ( x) 3x 5 2 h( x) 1200(.5) x We mean the same! y x 7 2 f ( x) x 7 2 Evaluating Functions To evaluate a function, simply replace (substitute) the function's variable with the indicated number or expression. Examples A function is represented by f (x) = 2x + 5. Find f (3). f (3) = 2(3) + 5 = 11 Find the value of when m= - 2 g (m) m 3m 11 3 2 g (2) (2) 3(2) 11 3 g (2) 15 2 A function is represented f (x) = -2x + 4. Find f (x + 6). f ( x 6) 2( x 6) 4 2 x 12 4 2 x 8 a) Evaluate f(-3) b) Evaluate f(0) f(x) Find the Domain and Range Graphically y 3x 1 y x2 4 y x 6x 4 2 1 y x 1 y x 1 1 y x 1 Work on Evaluating Functions with a Partner What did you notice about the domain? y 3x 1 D: all Real #’s 1 y x 1 D:{x | x 1} y x 1 y x2 4 D: all Real #’s D: {x | x 1} y y x2 6x 4 D: all Real #’s 1 x 1 D:{x | x 1} Restricted Domains The domain is all real numbers except when there is a… • Case 1: Variable in the Denominator – Set the denominator ≠ 0 and solve – Example: 3 • Find the Domain of y x4 x4 0 x4 Restricted Domains • Case 2: Variable under Square Root – Set the radicand ≥ 0 and solve – Example: Find the Domain of y x7 x7 0 x7 Restricted Domains • Case 3: Variable under Square Root AND in the denominator – Set the radicand in the denominator > 0 and solve 3 – Example: Find the domain of y x6 x60 x 6