When we say that the function f is increasing on 4 2

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Unformatted text preview: the following: This suggests4 the graph of f is symmetric about the y -axis, as expected. 2. g (x) = g (−x) = g (−x) = 5x 2 − x2 5(−x) 2 − (−x)2 −5x 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) 5x 2 − x2 −5x 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. 3. h(x) = h(−x) = h(−x) = 5x 2 − x3 5(−x) 2 − (−x)3 −5x 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 3 odd....
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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