Question

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

$\mathrm{y}=1-{\mathrm{x}}^2$

Answer 1

Given function: $\mathrm{y}=1-{\mathrm{x}}^2$

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

You can not write $\mathrm{y}=1-{\mathrm{x}}^2$ in slop intercept form.

So, the function does not have a constant rate of change. So, the function is nonlinear.

Hence, the function is nonlinear.