PP Section 3.2 - The Graph of a Function Definition When a...

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The Graph of a Function
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Definition When a function is defined by an equation in x and y, the graph of the function is the graph of the equation, that is, the set of all points (x,y) in the xy-plane that satisfies the equation.
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Examples Graph of y = 3x + 2 Graph of y = | x |
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A set of points in the xy -plane is the graph of a function if and only if any vertical line intersects the graph in at most one point. Vertical Line Test
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x y Example: Does the following graph represent a function? The graph does not represent a function, since it does not pass the vertical line test.
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Example: Does the following graph represent a function? The graph does represent a function, since it does pass the vertical line test. x y
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Learning from the Graph The graph of f(x) is given. Find the domain and range. Domain = [0, 9] Range = [1, 26] Estimate f(4) f(4) = 16
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Does the graph below represent a function? 4 0 -4 (0, -3) (2, 3) (4, 0) (10, -3) (1, 0) x y (7, -3) Yes
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For which x is f (x)=0? 4 0 -4 (0, -3) (2, 3) (4, 0) (10, -3) (1, 0) x y (7, -3) For x =1 and for x = 4.
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The following functions will be used throughout the text. Be able to recognize the shape of each graph
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This note was uploaded on 01/22/2011 for the course MATH 2 taught by Professor Gardner during the Fall '08 term at Irvine Valley College.

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PP Section 3.2 - The Graph of a Function Definition When a...

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