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FUNCTIONS RELATION: a set of ordered pairs EX 1: 0,0, 1,1, 2, 4, 3,9 EX 2: 2,3, 2,7 , 1, 4 DOMAIN: the set of all x-coordinates RANGE: the set of all y-coordinates FUNCTION: a relation in which each domain element corresponds to one and only one range element. *For every x, there is only 1 y. WAYS OF REPRESENTING 2,3, 2,7 , 1, 4 0,0,1,1,2,4 ,3,9 ORDERED PAIRS TABLE x 0 1 2 3 y 0 1 4 9 x 2 2 -1 y 3 7 4 GRAPH MAPPING DIAGRAM 0 1 2 3 0 1 4 9 2 -1 3 7 4 VERTICAL LINE TEST (VLT) If every vertical line intersects a given graph at no more than one point, then the graph represents a function. FUNCTION NOTATION f x 4x 1 y 4x 1 y f x f x "f is a function of x " x , y x ,f x EXAMPLE 1 Given y 4x 1 , evaluate f 5 , f 0 , f 7 . EXAMPLE 2 Find, f 4 . Find, f 1 . State the domain and the range. State any intercepts. Find any symmetry that exists with respect to the x-axis, y-axis, and/or origin. Example 3 Find f 4 . Find f 1 . State the domain and the range. State any intercepts. Find any symmetry that exists with respect to the x-axis, y-axis, and/or origin. Finding the Domain of a Function (1) For a polynomial, the domain is all real numbers. EX: (2) 5x3 2x2 6x 8 domain is all real numbers For expressions that contain radicals with even indices, the radicand must be greater than or equal to zero. 2x 3 EX: (3) 3 domain is , 2 For fractional expressions, the denominator cannot be equal to zero. x EX: domain is ,1 1, x 1 Examples State the domain for each of the following functions. EX 1: g x x3 1 EX 2: h x 3x 4 EX 3: p x 4x 2x 1 EX 4: q x x2 8x 12 EX 5: m x Function or Not a Function Graphically – VLT By Equation – 1. Try to solve for y in terms of x. 2. Decide whether each value of x corresponds to exactly one value of y. Example: Which of the equations represent(s) y as a function of x? a. x2 y 1 b. x y2 1 7 x 16 2