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# lecture3 - Lecture 3 1 Lecture 3 Section 2.1 Functions and...

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Lecture 3 1 Lecture 3: Section 2.1 Functions and Their Graphs Def. A function is a correspondence or rule which assigns to each element of a set A one and only one element in a set B . Set A : Set B : In this course, the domain and range of a function will be sets of real numbers only. ex.

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Lecture 3 2 Equations and Functions ex. Consider: y - x + 1 = 2 . 1. Is y a function of x ? 2. Domain: 3. Range:
Lecture 3 3 Graphs and Functions Consider the following graphs: Which represents y as a function of x ? Vertical Line Test : A graph represents y as a function of x if

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Lecture 3 4 ex. Consider the equation x 2 + y 2 = 4. Is y represented as a function of x ? Now look at y = 4 - x 2 and y = - 4 - x 2 .
Lecture 3 5 Function Notation A function is named: Then y = f ( x ) ex. Let f ( x ) = x + 1 + 2 1. f (0) = 2. f ( - 2) = ex. If g ( t ) = 2 + 3 t - t 2 , find g ( a + h ).

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Lecture 3 6 Finding the Domain of a Function ex. A farmer is to enclose a rectangular corral with 720 feet of fence. Express the area of the corral as a function of x , the width of the corral. What is the domain of the function?
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lecture3 - Lecture 3 1 Lecture 3 Section 2.1 Functions and...

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