Chapter 9.4, Problem 2CYP

To determine

To graph: The given function. Also, state the domain and range values in the context of the problem and the meaning of horizontal asymptote for the graph.

Explanation of Solution

Given information:

The following function:

  $S\left(x\right)=\frac{45x+25}{x+1}$ .

Graph:

Graph of the function is obtained as follows:

  

The vertical asymptote of the graph is calculated as follows:

  $\begin{array}{l}x+1=0[\text{Set }b(x)=0]\\ x=-1[\text{Subtract 1 from both sides]}\end{array}$

Graph the vertical asymptote of the function.Notice what happens to the y-axis values as x grows larger and as x gets smaller. The y-axis values approach $45$ . So, the equation for the horizontal asymptote is $S(x)=45$ .

In the problem context, years are non-negative values. Only values of x greater than or equal to $0$ and values of $S(x)$ between $0$ to $45$ are meaningful.