Answer: [tex]x^{3}[/tex] + 3x is an odd function and it is symmetric about the origin.
Step-by-step explanation:
A function is odd if the graph of the function is symmetrical about the origin, or a function is odd if f(-x) = -f(x). To determine if a function is even or odd, you substitute -x for x in the function, if the resulting function is the same as the original function, then the function is even but if otherwise , the function is odd. Considering the graph of [tex]x^{3}[/tex] + 3x , it is symmetric about the origin , therefore it is an odd function.
Considering the second method of checking , let us substitute -x for x in the equation.
[tex]x^{3}[/tex] + 3x
[tex](-x)^{3}[/tex] + 3(-x)
= [tex]-x^{3}[/tex] - 3x , this shows clearly that it is an odd function.
