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Unformatted text preview: the following: This suggests4 the graph of f is symmetric about the y -axis, as expected.
g (x) =
g (−x) =
g (−x) = 5x
2 − x2
2 − (−x)2
2 − x2 It doesn’t appear that g (−x) is equivalent to g (x). To prove this, we check with an x value.
After some trial and error, we see that g (1) = 5 whereas g (−1) = −5. This proves that g is
not even, but it doesn’t rule out the possibility that g is odd. (Why not?) To check if g is
odd, we compare g (−x) with −g (x)
2 − x2
2 − x2 −g (x) = −
= −g (x) = g (−x)
Hence, g is odd. Graphically,
4 ‘Suggests’ is about the extent of what it can do. 68 Relations and Functions The calculator indicates the graph of g is symmetric about the origin, as expected.
h(−x) = 5x
2 − x3
2 − (−x)3
2 + x3 Once again, h(−x) doesn’t appear to be equivalent to h(x). We check with an x value, for
example, h(1) = 5 but h(−1) = − 5 . This proves that h is not even and it also shows h is not
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