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Unformatted text preview: Chapter 3: Functions The Definition of a Function (3.1) Let A and B be nonempty sets. A function from set A to B is a rule of correspondence that assigns to each in set A exactly one element in set B. Examples: Set A Set B Set A Set B Net Work Viewer(s) War Year Manufacturer Model Person Birthday Pet Weight (lbs) Every element in set A has Exactly one element in B fails for one element in set B but Ford has no assignment the car and the pet’s weight example. The set A of inputs is called the domain of the function, and the set B of outputs is called the range. For example, for a equation y = 5 ξ + 1 , Table Graph x consists of domain values, y consists of the range values Following are the examples of what can or can’t be a domain value Find the domain of the following function: Ex 1: y = 1 3 τ + 12 , Interval notation: Set notation: Ex 2: y = 3 τ + 12 , Interval notation: Set notation: Ex 3: y = 3 τ + 12 3 , Ex 4: y = γ ( τ 29 = 1 τ 2 7 τ + 12 Interval notation: Set notation: The graph of a function (3.2) Definition: The graph of a function f in the xy plane consists of all those points (x, y) such that x is in the domain, and y = f(x) in the range How do you tell if a graph of f represents a function? Vertical Line Test: A graph in the xy plane represents y as a function of x if any vertical line intersects the graph in at most one point. Find if the following graphs represent a function. Justify your answer. Then find the domain and range if it represents a function. x 2 + ψ 2 = 1 y = φ ( ξ 29 = 25  ξ 2 f ( x ) = ξ Piecewise defined function: Look at the graphs 514, pg 153154 in your text book....
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 Spring '08
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