Determine whether the graph of the equation y=x3+x is symmetric with respect to the y-axis, the x-axis, the origin, or has no symmetry. Show your work.

Question

Determine whether the graph of the equation y=x3+x is symmetric with respect to the y-axis, the x-axis, the origin, or has no symmetry. Show your work.

Answer 1

A function f is symmetric about the y-axis if, f(x) = f(-x); origin symmetric if f(-x) = -f(x)

y(-x) = (-x)³ + (-x) = -x³ - x = - (x³ + x) = -y(x); no y-axis symmetry but origin symmetry

Since the function has origin symmetry, it cannot have x-axis symmetry as well.