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Published byDortha Cannon Modified over 9 years ago
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Testing for even and odd functions
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When the end points are included [ ]. When the end points are not included ( ). (4,8) Domain from (2, -3) to (5, -1) Written as [2, 5) Range [ -3, 8] open and close becomes a big deal (2, -3)(5,-1)
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Graphically using the Vertical line test. “ A set of points in a coordinate plane is the graph of y as a function of x iff no vertical line intersect the graph at more than one point.”Not a Function Function
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Zeros are the x’s that make f(x) = 0 Find the zero of the function f(x) = x 3 -4x 2 + 2x - 8 How do you find them?
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Zeros are the x’s that make f(x) = 0 Find the zero of the function f(x) = x 3 - 4x 2 + 2x - 8 How do you find them? Factoring would work
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f(x) = x 3 -4x 2 + 2x – 8 f(x) = x 2 (x - 4) + 2(x - 4)
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f(x) = x 3 -4x 2 + 2x – 8 f(x) = x 2 (x - 4) + 2(x - 4) f(x) = (x – 4)(x 2 + 2) 0 = (x – 4) and 0 = (x 2 + 2), 4 = x- 2 = x 2 thus the only real answer is x = 4
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We only worry about the numerator. 0 = 2a – 6 a = 3
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“Increasing” function x 1 f (x 1 ) “Decreasing” functionx 3 f (x 4 ) f(2) f(3) x 1 x 2 x 3 x 4
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Here f(2) f(3) x 1 x 2 x 3 x 4
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Over a Given Interval Minimum is the lowest point Maximum is the highest point. This will lead to the “Extreme Value Theorem”
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EVEN function is where f(x) = f(- x) Odd function is where f(- x) = - f(x) Let g(x) = x 3 + x thus ( -x) 3 + (- x) so - x 3 – x ; - g(x) = - (x 3 + x) It is then Odd f(x) = x 4 + 2 thus f(-x) = (-x) 4 + 2 ; x 4 + 2 which is the same as f(x)It is then Even
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Page 47-50 # 2, 10, 16, 22, 32, 54, 60, 62, 66, 86
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Page 47 – 50 #17, 23, 33, 37, 49, 55, 57, 61, 63, 83, 89
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