Chapter 8.3, Problem 47PPSE

Solution

To identify: The condition that will produce a rational function with a graph that has no vertical asymptotes.

If the denominator has no zeros or all the zeroes of the denominator are also the zeros of numerator with same multiplicity, then the rational function.

Given information:

The statement: Describe the condition that will produce a rational function with a graph that has no vertical asymptotes.

Explanation:

Consider the given information.

Asymptotes are lines that a curve approaches as it approaches infinity.

There are two possible cases:

Case 1: If the denominator of rational function has no zeros, then the rational function has no vertical asymptotes.

Case 2: If all the zeroes of the denominator are also the zeros of numerator with same multiplicity, then the rational function has no vertical asymptotes. In this case zeroes are the holes of the graph.