Chapter 1.2, Problem 64E

Solution

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

  

The correct match is Graph(c).

Given information: 

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

Calculation:

Consider the function

  $y=\frac{x^2+2}{2x+1}$

A vertical asymptote is anticipated at $x=-\frac{1}{2}$ , the function is undefined for that value of

  $x$ (Division by zero).

As the numerator is of a higher degree than the denominator, the function is expected to continue to grow to positive infinity or negative infinity.

This closely matches the behavior of graph(c).

Hence, the match graph is graph(c).