Section 2.4 Functions and graphs

This is called the natural domain of the function two

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Unformatted text preview: e function. Two cases where f (x ) may not be defined as a real number are: 1 2 Points x for which division by zero occurs. Points x for which a negative even root occurs. Outline Functions Representing Functions The Domain and Range Evaluating Functions Examples Example Find the domain and range of each of the following. 1 f (x ) = x 2 2 f (x ) = 3 x . −4 √ f (x ) = 3x − 1. x2 Average Rate of Change Outline Functions Representing Functions The Domain and Range Evaluating Functions Average Rate of Change Evaluating a Function Let f : D → Y be a function. We evaluate f at a point x = c if we replace all variables x in the expression for f (x ) by the number c . The output is denoted y = f (c ). Example Evaluate the function f (x ) = 3x 2 − 4x at x = 0, −1, 1, 2, 2c , c + 1. Outline Functions Representing Functions The Domain and Range Evaluating Functions Average Rate of Change The Average Rate of Change of a Function Definition Suppose f is a function that is continuous on an interval [a, b ]. The average rate of change of f on [a, b ] is the number ∆y f (b ) − f (a) = . ∆x b−a This is the slope of the secant line that goes through the points (a, f (a)) and (b , f (b )). Example #102 in the book....
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