Question

Does the equation represent a linear or nonlinear function? Explain.

$\mathrm{y}=\frac{8}{{\mathrm{x}}^2}$

Answer 1

A linear function can be described by a linear equation and a linear equation is a degree-$1$ polynomial.

Also, a linear equation has the form: $\mathrm{y}=\mathrm{mx}+\mathrm{c}$ where $\mathrm{m}$ is the slope, $\mathrm{c}$ is the constant.

Given equation : $\mathrm{y}=\frac{8}{{\mathrm{x}}^2}$

Here, the equation is not a linear function because the term $\frac{8}{{\mathrm{x}}^2}$ has degree $2$ and also not in the form of $\mathrm{y}=\mathrm{mx}+\mathrm{c}$.

Hence, the equation represents a nonlinear function.