Answer
x-intercepts at (0,0),(2,0), and (-2,0)
y-intercept at (0,0)
symmetric to origin
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.
