Expert: Steve Holleran - 12/10/2007

Question
Determine whether the graph of each relation is symmetric with respect to the xaxis y axis and the origin
Y=xcubed plus 6x
Y=xto the fourth power plus x squared

Answer
Hi Pam,


The idea here is to form f(-x) and compare it to the original.  If its the same, you have y-axis symmetry, if its the opposite, you have origin symmetry.  These are both functions , so neither would have x-axis symmetry (because then they wouldn't be functions).

1.  y = x^3 + 6x

Form y(-x):  (-x)^3 + 6(-x) = -x^3 - 6x

This is the opposite of the original, so it has origin symmetry.

2.  y = x^4 + x^2

y(-x) = (-x)^4 + (-x)^2 = x^4 + x^2

This is the same as the original, so it has y-axis symmetry

Neither have x-axis symmetry

Steve