   Chapter 10, Problem 20RE ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 20 and 21, find any horizontal asymptotes and any vertical asymptotes. y = 3 x + 2 2 x − 4

To determine

To calculate: The horizontal and vertical asymptote, for the function y=3x+22x4.

Explanation

Given Information:

The provided function is y=3x+22x4.

Formula used:

A vertical asymptote of a function f(x) is a line x=a such that f(a)=.

A vertical asymptote of a rational function h(x)=f(x)g(x) is x=a where g(a)=0 and f(a)0.

A horizontal asymptote of a function f(x) is a line y=b such that limxf(x)=b or limxf(x)=b.

A horizontal asymptote of a rational function h(x)=f(x)g(x) is

1. A line y=0 if the degree of the numerator is less than the degree of the denominator.

2. The line y is ratio of the leading coefficients if the degree of the numerator is equal to the degree of the denominator.

3. Does not exist if the degree of the numerator is greater than the degree of the denominator.

Calculation:

Consider the provided function,

y=3x+22x4

Recall that a vertical asymptote of a rational function h(x)=f(x)g(x) is x=a where g(a)=0 and f(a)0

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