In our case the numerator is one and will never be

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Unformatted text preview: axis. y = 2( -x) - ( -x) 3 5 y = -2 x 3 + x 5 Remember that if we take a negative to an odd power the minus sign can come out in front. So, upon simplifying we get the left side to be identical to the original equation, but the right side is now the opposite sign from the original equation and so this isn’t equivalent to the original equation and so we don’t have symmetry about the y-axis. Finally, let’s check symmetry about the origin. © 2007 Paul Dawkins 235 College Algebra - y = 2( -x) - (-x) 3 5 - y = -2 x 3 + x 5 Now, this time notice that all the signs in this equation are exactly the opposite form the original equation. This means that it IS equivalent to the original equation since all we would need to do is multiply the whole thing by “-1” to get back to the original equation. Therefore, in this case we have symmetry about the origin. [Return to Problems] (c) y 4 + x 3 - 5 x = 0 First, check for symmetry about the x-axis. (- y) 4 +...
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