When a rational function has no vertical asymptotes

The video tutorial explains how to identify vertical asymptotes in rational functions by focusing on non-removable discontinuities where the denominator equals zero. It highlights that vertical asymptotes occur when the function is undefined for real numbers. In this problem, solving the equation results in imaginary numbers, indicating no vertical asymptote exists for real numbers.

What is a vertical asymptote in a rational function?

• A point where the denominator is zero and cannot be removed

• A point where the function is undefined for imaginary numbers

• A point where the numerator is zero

• A point where both numerator and denominator are zero

What happens to the function at a vertical asymptote?

• The function becomes infinite

• The function becomes undefined

• The function becomes zero

• The function becomes continuous

When solving for vertical asymptotes, what type of solutions do not affect the real number domain?

• Imaginary solutions

• Rational solutions

• Complex solutions

• Real solutions

What is the significance of the domain in determining vertical asymptotes?

• It includes all complex numbers

• It includes all real numbers where the function is defined

• It includes only imaginary numbers

• It excludes all real numbers

Why is there no vertical asymptote in the given problem?

• Because the denominator is zero for real numbers

• Because the numerator is zero for real numbers

• Because the function is continuous

• Because the solutions are imaginary