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# 1.1fill - Example 2 Suppose x x x f-= 7 Find x f 1 2-and...

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Section 1.1 – Definition of a Function 1 Section 1.1 Definition of a Function Let A and B be two nonempty sets. A function from A to B is a rule of correspondence that assigns to each element in A exactly one element in B. Domain of a Function To determine the domain of a function, start with all real numbers and then eliminate anything that results in zero denominators or even roots of negative numbers. Range of a Function To determine the range of a function, determine what outputs are possible. This is not always easy. Sometimes it helps to graph the function. Example 1: Find the domain for each of the following functions. a. 5 2 - = x ) x ( f b. 7 1 4 - + + + = x x ) x ( f and then find the range.

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Section 1.1 – Definition of a Function 2 c. 20 9 6 2 2 + + + - + + + = x x x ) x ( f d. 7 1 3 2 1 + + + - + + + + + + = x x x ) x ( f e. 12 7 3 + + + = x x ) x ( f
Section 1.1 – Definition of a Function 3 Evaluating Functions

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Unformatted text preview: Example 2: Suppose x x ) x ( f-= 7 . Find ) x ( f 1 2 + + +-and then its y-intercept. Piecewise Defined Functions Definition: A function that is defined by two (or more) equations over a specified domain is called a piecewise function. Example 3: Suppose ≥ < <---≤-= 8 8 2 5 2 3 2 x , x x , x , x ) x ( f . Find: a. f(-10) b. f(15) c. y-intercept Section 1.1 – Definition of a Function 4 Average Rate of Change h ) x ( f ) h x ( f x ) h x ( ) x ( f ) h x ( f x y x in change y in change-+ + + =-+ + +-+ + + = ∆ ∆ = This is the Difference Quotient and it will be used in Calculus. Example 4: Calculate the Difference Quotient of 1 1 + + + = x ) x ( f . Example 5: Calculate the Difference Quotient of x x ) x ( f--= 2...
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1.1fill - Example 2 Suppose x x x f-= 7 Find x f 1 2-and...

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