Question

Jeanne claims that an equation of the form y=xn+28.3, where n is a whole number, represents a nonlinear function. Describe all values of n for which Jeanne's claim is true and all values of n for which Jeanne's claim is false. Explain.Bn

Answer 1

ANSWER

Jeanne's claim is true for n≥2

Jeanne's claim is false for n=0 and n=1

EXPLANATION

The given equation is

$y = {x}^{n} + 28.3$

where n is a whole number.

This equation is nonlinear for

$n\ge2$

In this case Jeanne's claim is true

But when n=0 or n=1, Jeanne's claim is false.

The reason is that, when n=0, the equation becomes

$y = 28.3$

which is a constant function.

When n=1, the equation becomes

$y = x + 28.3$

which is a linear function.