IB Maths AA HL Ahl 2 14 Hl Odd Even and Inverse Functions Topic Practice

The following question explores features of a family of curves. The family is then linked to a homogeneous differential equation.
Consider the curve given by $y=\frac{x\left(x^{2}-16\right)}{x^{2}+16}$.

State whether the function $f(x)=\frac{x\left(x^{2}-16\right)}{x^{2}+16}$ is odd, even or neither. Justify your answer. [2]

Now consider the general curve given by $y=\frac{x\left(x^{2}-A\right)}{x^{2}+A}$, where A is a positive constant
and $x \in \mathbb{R}$. and $x \in \mathbb{R}$.