Chapter 10.5, Problem 3E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

In Problems 1-4, a function and its graph are given. Use the graph to find each of the following, if they exist. Then confirm your results analytically.

(a) vertical asymptotes

**(b)**

**(c)**

(d) horizontal asymptotes

**(a)**

To determine

The vertical asymptote for the function

Also, verify the result analytically.

Explanation

**Given Information:**

The provided graph of the function

.

**Explanation:**

A vertical asymptote of a function

Consider the provided graph,

From the graph, at

Thus, the vertical asymptotes are the lines

A vertical asymptote of a rational function

Now, consider the function

Set the denominator of the function equal to 0.

Take square root on both sides.

Thus, the possible vertical asymptotes are the lines

**(b)**

To determine

The value of

Also, verify the result analytically.

**(c)**

To determine

The value of

Also, verify the result analytically.

**(d)**

To determine

The horizontal asymptote for the function

Also, verify the result analytically.

Sect-10.1 P-1CPSect-10.1 P-2CPSect-10.1 P-3CPSect-10.1 P-4CPSect-10.1 P-1ESect-10.1 P-2ESect-10.1 P-3ESect-10.1 P-4ESect-10.1 P-5ESect-10.1 P-6E

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