   Chapter 3.4, Problem 46E

Chapter
Section
Textbook Problem

# Find a formula for a function that has vertical asymptotes x = 1 and x = 3 and horizontal asymptote y = 1 .

To determine

To find:

A formula for a function that has vertical asymptotes x=1 and x=3 and horizontal asymptote y=1

Explanation

1) Concept:

Use definitions of horizontal and vertical asymptote.

2) Definitions:

Horizontal asymptote:

Horizontal asymptote: y=b

As x±, yb or limx±∞ f(x)=b

Vertical asymptote:

Vertical asymptote: x=c

As xc, y± or limxcf(x)=±

3) Calculation:

By the definition of vertical asymptote at x=1 and x=3 denominator is 0

It means limx1f(x)= or- and

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