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One quantity depends on another quantity # of shirts -> revenue Age -> Height Time of day -> Temperature 3.1 Function
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Function-Definition 4 Representations of a function: Verbally – Numerically – Algebraically – Visually – Formal definition: A function f is a rule that assigns to each element x in a set A exactly one element, f(x), in a set B. ( f(x) is read as “ f of x ”)
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Verbal & Numeric Verbal: Function f(x) divides x by 3 and then adds 4. A B Numeric: x-259-41 f(x) Table describes the values in A and their assignments in B.
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Algebraic & Graphic Algebraic: Graphic: x-259-41 f(x)4142-3275 Plot points (x, f(x)) in the two dimensional plane 2468 -21 21 42 x f(x)
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Example: Evaluate the function at the indicated values.
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Piecewise Functions Evaluate the function at the indicated values.
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Difference Quotient Find f(a), f(a+h), and the difference quotient for the given function. Difference quotient:
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Domain Domain: the set of all inputs for which the function is a real number. (valid x) Recall definition: A function f is a rule that assigns to each element x in a set A exactly one element, f(x), in a set B. Set A = input => x = independent variable Set B = output => y = f(x) = dependent variable Two restrictions on the domain for any function :
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Example 1 Find the domain for the following function. D:
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Example 2 Find the domain for the following function. D:
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