Answer
True
Work Step by Step
For an odd function, we have:
$f(-x)=-f(x)$
We test if $f(x)=x^3$ is an odd function:
$f(-x)=(-x)^3=-(x^3)=-f(x)$
Thus, the cube function, $f(x)=x^3$ is an odd function.
We know that for $x\gt 0$, the cube function $x^3$ is always increasing because a larger number cubed is greater than a smaller number cubed. Similarly, for $x\lt 0$, the cube function is also always increasing because a smaller negative number cubed is larger than a large negative number cubed. Thus, the function is increasing on the interval $(-\infty,\infty)$. So, the statement is True.
