2 the line y b is a horizontal asymptote if the graph

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Unformatted text preview: x3 - 5 x = 0 y 4 + x3 - 5 x = 0 This is identical to the original equation and so we have symmetry about the x-axis. Now, check for symmetry about the y-axis. y4 + ( -x ) - 5( -x ) = 0 3 y 4 - x3 + 5 x = 0 So, some terms have the same sign as the original equation and other don’t so there isn’t symmetry about the y-axis. Finally, check for symmetry about the origin. (- y) + (-x) 4 3 - 5(-x) = 0 y 4 - x3 + 5 x = 0 Again, this is not the same as the original equation and isn’t exactly the opposite sign from the original equation and so isn’t symmetric about the origin. [Return to Problems] (d) y = x3 + x 2 + x + 1 First, symmetry about the x-axis. - y = x3 + x2 + x + 1 It looks like not symmetry about the x-axis Next, symmetry about the y-axis. y = (-x) + (-x) + ( -x) +1 3 2 y = - x3 + x2 - x + 1 So, no symmetry here either. Finally, symmetry about the origin. © 2007 Paul Dawkins 236 http://tutorial.math.lamar.edu/terms.aspx College Algebra - y = (-x) + ( -x) + (-x) +1 3 2 - y = - x3 + x2 - x + 1 A...
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