lecture3 - Lecture 3 Elementary Functions Sec 1.1 and 1.2...

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Lecture 3: Elementary Functions Sec. 1.1 and 1.2 Def. A function f is a rule which assigns to each element x in set D exactly one element, called f ( x ), in a set E . Set D Set E We deﬂne functions in several ways:

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ex. A closed box with a square base has a surface area of 128 square inches. Express the volume of the box as a function of the length of the edge of the base. What is its domain?
ex. Find the domain of each function: 1) f ( x ) = 2 x 2 ¡ 4 x 2) g ( x ) = p x 2 + 5 x ¡ 6

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Def. The graph of a function f ( x ) is the set of ordered pairs ( x;y ) in the coordinate plane such that x is in the domain of f and y = f ( x ). Consider the graphs below. Which represent y as a function of x ? 6 - ? ± 6 - ? ± 6 - ? ± Vertical Line Test
Piecewise Deﬂned Functions Absolute Value Recall: f ( x ) = j x j = 8 < : x < 0 x 0 ex. Sketch the following graphs: 1) f ( x ) = j 2 x j ¡ x 6 - ? ± 2) g ( x ) = j x j x 6 - ? ±

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ex. Sketch the graph: g ( x ) = 8 > > < > > : x + 1 x < 0 1 0 < x 2 4 ¡ x x > 2 6 - ? ±
Even Functions Odd Functions ex. Determine whether f ( x ) = x ¡ x 3 is even, odd, or neither.

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Def. A function f
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lecture3 - Lecture 3 Elementary Functions Sec 1.1 and 1.2...

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