Chapter 6.8, Problem 10SGR

To determine

Whether the statement “ ${\left(x^3\right)}^2+3x^3-8=0$ is a $\text{power function}$ .” is true or false.

Answer to Problem 10SGR

The statement “ ${\left(x^3\right)}^2+3x^3-8=0$ is a $\text{power function}$ .” is false.

Explanation of Solution

Given information:

The statement “ ${\left(x^3\right)}^2+3x^3-8=0$ is a $\text{power function}$ .”

Consider the provided statement “ ${\left(x^3\right)}^2+3x^3-8=0$ is a $\text{power function}$ .”

This ${\left(x^3\right)}^2+3x^3-8=0$ is written in a quadratic form.

The power function is in the form of $f\left(x\right)=k{x}^n$ , where $k=\text{all real numbers and n}=\text{all real numbers}$ you can change the way the graph of power function looks of $k\text{ and }n$ .

In a quadratic form the equation is in the form of:

  $x^4+x^3+x^2+1$

Thus, the statement “ ${\left(x^3\right)}^2+3x^3-8=0$ is a $\text{power function}$ .” is false.