Question

1. does the equation represent a linear or nonlinear function? explain. $y = \frac{8}{x^2}$

Explanation:

Step1: Rewrite the given equation

$y = 8x^{-2}$

Step2: Check linear function criteria

A linear function has the form $y=mx+b$, where the exponent of $x$ is 1. Here, the exponent of $x$ is $-2$, which is not 1.

Answer:

The equation represents a nonlinear function. A linear function must have the independent variable raised to the first power only, but this equation can be rewritten as $y = 8x^{-2}$, where $x$ has an exponent of $-2$, so it does not meet the requirements of a linear function.