Section_2.2-Graphs of Functions

Section_2.2-Graphs of Functions - y = x 2 . If x > 1 ,...

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Section 2.2 Graphs of Functions DEFINITION: A function f is a rule that assigns to each element x in a set A exactly one element, called f ( x ) , in a set B . It’s graph is the set of ordered pairs { ( x, f ( x )) | x A } EXAMPLE: Sketch the graphs of the following functions. (a) f ( x ) = x 2 (b) g ( x ) = x 3 (c) h ( x ) = x Solution: We first make a table of values. Then we plot the points given by the table and join them by a smooth curve to obtain the graph. The graphs are sketched in the Figures below. EXAMPLE: Sketch the graph of the function. f ( x ) = { x 2 if x 1 2 x + 1 if x > 1 1
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EXAMPLE: Sketch the graph of the function. f ( x ) = { x 2 if x 1 2 x + 1 if x > 1 Solution: If x 1 , then f ( x ) = x 2 , so the part of the graph to the left of x = 1 coincides with the graph of
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Unformatted text preview: y = x 2 . If x > 1 , then f ( x ) = 2 x +1 , so the part of the graph to the right of x = 1 coincides with the line y = 2 x + 1 . EXAMPLE: Sketch the graph of the function f ( x ) = | x | . Solution: Recall that f ( x ) = { x if x -x if x < Using the same method as in the previous example, we note that the graph of f coincides with the line y = x to the right of the y-axis and coincides with the line y =-x to the left of the y-axis. EXAMPLES: 2 EXAMPLE: Which of the following are graphs of functions? Solution: (a) and (b) are graphs of functions, (c) and (d) are not. 3 4...
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This note was uploaded on 02/26/2012 for the course MATH 8650 taught by Professor Kiryltsishchanka during the Spring '12 term at NYU.

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Section_2.2-Graphs of Functions - y = x 2 . If x > 1 ,...

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