Chapter 11.3, Problem 76E

Solution

To find: The correct graph for the function $y=\frac{x^2+2x+3}{x-3}$ .

Graph (a)

Given information:

The given function is $y=\frac{x^2+2x+3}{x-3}$ .

Calculation:

The function is undefined for $x=3$ . So we can eliminate option (e).

  $y=\frac{x^2+2x+3}{x-3}$

As $x$ approaches 5 from the left, the numerator is positive (it is always positive) and the denominator is negatively' small. So, the function is negatively large.

As $x$ approaches 5 from the right, the numerator is positive (it is always positive) and the denominator is positively mall. So, the function is positively large. This matches to graph (a).