Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter P - P.1 - Graphs and Models - Exercises: 44

Answer

x-intercepts at (0,0),(2,0), and (-2,0) y-intercept at (0,0) symmetric to origin
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Work Step by Step

x-int 0=$x^{3}$-4x 0=x($x^{2}$-4) x=0,2,-2 x-intercepts at (0,0),(2,0), and (-2,0) y-int y=$0^{3}$-4(0) y=0 y-intercept at (0,0) Find Symmetry: Substitute -x for x. If equation is equivalent, graph is symmetric to y-axis. y=$(-x)^{3}$-4(-x) y=$-x^{3}$+4x Equations are not equivalent, so not symmetric to y-axis. Substitute -y for y. If equation is equivalent, graph is symmetric to x-axis. (-y)=$x^{3}$-4x y=$-x^{3}$+4x Equations are not equivalent, so not symmetric to x-axis. Substitute -y for y and -x for x. If equation is equivalent, graph is symmetric to origin. (-y)=$(-x)^{3}$-4(-x) y=$x^{3}$-4x Equations are equivalent, so function is symmetric to origin.
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