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Define Even and Odd functions algebraically and graphically

Define Even and Odd functions algebraically and graphically. Continue …. Example 1. Check whether the following graphs represent an even or odd functions or neither. a). c). The graph represents an even function. The graph represents neither. b). d). The graph represents neither.

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Define Even and Odd functions algebraically and graphically

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  1. Define Even and Odd functions algebraically and graphically

  2. Continue… Example 1 Check whether the following graphs represent an even or odd functions or neither. a) c) The graph represents an even function The graph represents neither b) d) The graph represents neither The graph represents an odd function

  3. Even and Odd Functions Example 1 Determine whether a function is even, odd or neither. a) f ( x ) = 3x4 + 5x2 –4 b) f( x ) = -2x5 +4x3 +7x c) f( x ) = x5 +x2 Substitute x by –x f(-x) = -2 (-x)5 + 4( -x )3 +7(-x) = 2x5 – 4x3 – 7x = - (-2x5 +4x3 +7x ) = - f(x) f(-x) = - f(x) f is odd Solution: Substitute x by –x f(-x) = ( -x )5 + ( -x )2 = - x5 + x2 f(-x) is not equal to f( x) nor –f(x). Therefore, f is neither. • Substitute x by –x • f( -x) = 3( -x )4 + 5 ( -x )2 - 4 • = 3x4 + 5x2 – 4 • = f(x) • f( -x) = f(x) • f is even.

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