The vertical asymptotes of the rational function r(x)=(x+1)(x−2)(x+2)(x−3)

Expert Solution & Answer

Answer to Problem 5E

The vertical asymptotes of the rational function r(x)=(x+1)(x−2)(x+2)(x−3) are x=−2 and x=3 .

Explanation of Solution

Given:

The given rational function is,

r(x)=(x+1)(x−2)(x+2)(x−3)

Calculation:

The vertical asymptote is a vertical line where the graph is approaches towards that line but not equal to the line at any point.

The vertical asymptote occurs where the function is not defined for the value or the denominator value is zero.

Take denominator equal to zero, to find the vertical asymptote.

(x+2)(x−3)=0

Simplify the above expression,

x+2=0x=−2

And

x−3=0x=3

Thus, the vertical asymptotes of the rational function r(x)=(x+1)(x−2)(x+2)(x−3) are x=−2 and x=3 .

Chapter 3.7, Problem 4E

Chapter 3.7, Problem 6E

Chapter 3 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

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The vertical asymptotes of the rational function r(x)=(x+1)(x−2)(x+2)(x−3)

Answer to Problem 5E

Explanation of Solution

Chapter 3 Solutions