Chapter 1.2, Problem 63E

Solution

To find: match the function with the corresponding graph by considering end behavior and asymptotes.

  

The correct match is Graph(b).

Given information: 

The function $y=\frac{x+2}{2x+1}$ .

Calculation:

Consider the function

  $y=\frac{x+2}{2x+1}$ .

A vertical asymptote is anticipated at $x=-\frac{1}{2}$ the function is undefined for that value of $x$ (division by zero).

And $x$ become infinitely large, the function will approach a constant, $+2$ and $+1$ becomes irrelevant and $y$ approaches $\frac{x}{2x}=\frac{1}{2}$ .

This closely matches the behavior of graph (b).

Hence, the match graph is graph(b)