mac1147_lecture10_1_b

mac1147_lecture10_1_b - L10 Graphs, Properties, and Library...

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117 L10 Graphs, Properties, and Library of Functions; Graphing Techniques: Transformations The graph of a relation in x and y is the set of all points in the xy -plane that correspond to the ordered pairs ( , ) x y . If a relation is a function, then for every x in the domain there is only one y , ( ) yf x = , in the range. With respect to the graph it means that a vertical line x a = either intersects the graph at one point ( , ( )) afa (if a is in the domain of f ) or x a = does not intersect the graph at all (if a is not in the domain of the function). Thus, we have obtained: Vertical Line Test A set of points ( , ) x y in the xy -plane is the graph of a function if and only if every vertical line intersects the graph at no more than one point.
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118 Example: Use the vertical line test to determine which of the graphs given below represent functions.
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119 Even and Odd Functions A function () f x is called even if, for every x in the domain of f , x is also in the domain and ( ) fx f x = . The graph of an even function is symmetric with respect to the y-axis . 2 x = A function f x is called odd if, for every x in the domain of f , x is also in the domain and ( ) f x =− .
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mac1147_lecture10_1_b - L10 Graphs, Properties, and Library...

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