Question 887071: Determine whether the graph of y=x^3 - 5x is symmetric with respect to the x-axis, the y-axis, or the origin.
Please show the work so I can see how the problem was worked out. Thanks
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! here's some references on this:
http://tutorial.math.lamar.edu/Classes/Alg/Symmetry.aspx
http://www.mathsisfun.com/algebra/equation-symmetry.html
http://www.purplemath.com/modules/symmetry3.htm
the equation is symmetric about the x-axis if (x,y) = (x,-y)
the equation is symmetric about the y-axis if (x,y) = (-x,y)
the equation is symmetric about the origin if (x,y) = (-x,-y)
equation is y = x^3 - 5x
to test if the equation is symmetric about the x-axis, replace y with -y and solve for y.
you get -y = x^3 - 5x
multiply both sides of this equation by -1 and you get:
y = -x^3 + 5x
since y = -x^3 + 5x is not the same equation as y = -x^3 + 5x, your equation is not symmetric about the x-axis.
to test if the equation is symmetric about the y-axis, replace x with -x and solve for y.
you get y = (-x)^3 - 5(-x)
simplify to get:
y = -x^3 + 5x
since y = -x^3 + 5x is not the same equation as y = -x^3 + 5x, your equation is not symmetric about the y-axis.
to test if the equation is symmetric about the origin, replace x with -x and y with -y and solve for y.
you get -y = (-x)^3 - 5(-x)
simplify to get:
-y = -x^3 + 5x
multiply both sides of the equation by -1 and you get:
y = x^3 - 5x
since y = x^3 + 5x is the same equation as y = x^3 - 5x, your equation is symmetric about the origin.
a graph of your equation is shown below:
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