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14209an2.1-5

# 14209an2.1-5 - c Kendra Kilmer Section 2.1 Functions...

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c circlecopyrt Kendra Kilmer January 20, 2009 Section 2.1 - Functions Example 1: Sketch a graph for each of the following equations: a) 2 x + y = 8 b) x 2 + y 2 = 1 c) y = x 2 + 1 Which of the above are functions? 1

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c circlecopyrt Kendra Kilmer January 20, 2009 Definition: A function is a rule that assigns to each element x in the domain exactly element in the range. The is the set of all values of the independent variable (typically x ) that produce real values for the dependent variable (typically y ). The is the set of all possible y values as x varies throughout the domain. Example 2: Find the domain and range of each function in Example 1. Vertical Line Test: An equation defines a if each vertical line in the coordinate system passes through at most one point on the graph of the equation. Example 3: Determine whether each is a function of x . a) 4 2 -2 -4 -2 -4 2 4 b) 2 4 -4 2 4 -2 -2 -4 c) -2 -4 -2 -4 2 4 2 4 2
c circlecopyrt Kendra Kilmer January 20, 2009 Function Notation: If the correspondence is a function we use the notation f ( x ) read “ f of x ”. Ordered pairs of the form ( x , y ) can be written as ( x , f ( x )) . Example 4: Let k ( x ) = x 2 + 2 x 1 and g ( x ) = 1 x . Find the following:

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14209an2.1-5 - c Kendra Kilmer Section 2.1 Functions...

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