Chapter 1, Problem 34RE

(a)

To determine

To find: The power function of end behavior model.

Answer to Problem 34RE

2 is the power function of end behavior model.

Explanation of Solution

Given information: The function is $f(x)=\frac{2x^2+5x-1}{x^2+2x}$

Calculation:

The given fraction is :

  $f(x)=\frac{2x^2+5x-1}{x^2+2x}$

In the chapter "End behavior model" that the highest powers in the denominator and numerator are the only ones we need to look at in order to find a power function end behavior model. The highest powers and their corresponding coefficients in the numerator and denominator in this case are $2x^2$ and $x^2$ , respectively,

  $\begin{array}{c}\frac{2x^2}{x^2}=\frac{2}{1}\\ =2\end{array}$

Therefore, the power function of end behavior model is 2.

(b)

To determine

To find: The horizontal asymptote.

Answer to Problem 34RE

  $y=2$ is the horizontal asymptote.

Explanation of Solution

Given information: The function is $f(x)=\frac{2x^2+5x-1}{x^2+2x}$

Calculation:

The given fraction is :

  $f(x)=\frac{2x^2+5x-1}{x^2+2x}$

In the end behavior model, what happens as $x$ approaches infinity must be observed in order to determine the horizontal asymptote. Given that the end behavior model is 2, horizontal asymptotes can be found by:

Infer that $y=2$ is the horizontal asymptote from this.

Divide the coefficients of the terms with the highest degree if both polynomials have the same degree.

Therefore, $y=2$ is the horizontal asymptote.