Unformatted text preview: (−x), so i is even. The calculator supports our conclusion. 5.
x
−1
100
−x
j (−x) = (−x)2 −
−1
100
x
−1
j (−x) = x2 +
100
j (x) = x2 − The expression for j (−x) doesn’t seem to be equivalent to j (x), so we check using x = 1 to
1
1
get j (1) = − 100 and j (−1) = 100 . This rules out j being even. However, it doesn’t rule out
j being odd. Examining −j (x) gives
x
−1
100
x
−j (x) = − x2 −
−1
100
x
−j (x) = −x2 +
+1
100
j (x) = x2 − The expression −j (x) doesn’t seem to match j (−x) either. Testing x = 2 gives j (2) =
and j (−2) = 151 , so j is not odd, either. The calculator gives:
50 149
50 70 Relations and Functions The calculator suggests that the graph of j is symmetric about the y axis which would imply
that j is even. However, we have proven that is not the case.
There are two lessons to be learned from the last example. The ﬁrst is that sampling function
values at particular x values is not enough to prove that a function is even or odd...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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