Chapter 2.2, Problem 64E

To determine

Tochoose:The correct option for the end behavior model for $f\left(x\right)=\frac{2x^3-x^2+x+1}{x^3-1}$ .

Answer to Problem 64E

The correct choice is (D) such that the end behavior model of $f\left(x\right)=\frac{2x^3-x^2+x+1}{x^3-1}$ is $2$ .

Explanation of Solution

Given information:

The functionis $f\left(x\right)=\frac{2x^3-x^2+x+1}{x^3-1}$ .

The given function $f\left(x\right)=\frac{2x^3-x^2+x+1}{x^3-1}$ is a polynomial function.

The power function end behavior model of a polynomial function is the highest power term.

The power function end behavior model of the numerator is $2x^3$ and the denominator ofis $x^3$ .

So, the power function end behavior model of the function $f\left(x\right)=\frac{2x^3-x^2+x+1}{x^3-1}$ is:

  $\frac{2x^3}{x^3}=2$

Therefore, the correct choice is (D) such that the end behavior model of $f\left(x\right)=\frac{2x^3-x^2+x+1}{x^3-1}$ is $2$ .