M1410105Part2

# M1410105Part2 - (Section 1.5 Analyzing Graphs of Functions...

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(Section 1.5: Analyzing Graphs of Functions) 1.51 PART F: FUNCTIONS THAT ARE EVEN / ODD / NEITHER; SYMMETRY A function f is even f x ( ) = f x ( ) x Dom f ( ) for every x in the domain of f   The graph of y = f x ( ) is symmetric about the y - axis . (We will discuss this in the following Example.) Example If f x ( ) = x 2 , then f is even, because x R , f x ( ) = x ( ) 2 = x 2 = f x ( ) The “bowl” graph of f x ( ) y = x 2 below is symmetric about the y -axis. This means that the parts of the graph to the right and to the left of the y -axis are mirror images (or reflections) of each other. See Section 1.7, Notes 1.82 . More formally, the point x , y ( ) lies on the graph if and only if the point x , y ( ) does.

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(Section 1.5: Analyzing Graphs of Functions) 1.52 The term “even function” may have come from the following fact: If f x ( ) = x n , where n is an even integer, then f is an even function. These are the functions for: , x 4 , x 2 , x 0 , x 2 , x 4 , . We will discuss these further in Section 1.6 . The graph for the x 2 function on the previous page is called a parabola. However, the graphs for x 4 , x 6 , etc. are not parabolas. We will discuss parabolas more in Chapter 2 . The reciprocal of a nonzero even function is even. Example The functions for both x 2 and x 2 which equals 1 x 2 are even. Example (also see Chapter 4 ) The graph of the even function f x ( ) = cos x is below.
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