Identify any horizontal or vertical asymptotes of a rational function

The video tutorial explains how to find horizontal and vertical asymptotes of a function. It begins with an introduction to asymptotes, followed by a detailed explanation of the horizontal asymptote test, which involves comparing the exponents of the leading terms in the numerator and denominator of a polynomial. The tutorial then discusses vertical asymptotes, focusing on domain constraints and the conditions under which vertical asymptotes do not exist. The video concludes with a summary of the key points covered.

What is the first step in determining the horizontal asymptote of a rational function?

• Set the denominator equal to zero.

• Compare the coefficients of the leading terms.

• Find the square root of the numerator.

• Ensure the polynomials are in descending order.

When the exponents of the leading terms in the numerator and denominator are equal, how is the horizontal asymptote determined?

• By adding the exponents.

• By subtracting the coefficients.

• By dividing the leading coefficients.

• By multiplying the coefficients.

What does a vertical asymptote represent in terms of a function's domain?

• A point where the function equals zero.

• A point where the function is continuous.

• A point where the function is undefined.

• A point where the function has a maximum.

In the given example, why are there no vertical asymptotes?

• Because the exponents are different.

• Because the denominator cannot be zero.

• Because the coefficients are equal.

• Because the numerator is zero.

What is the domain of the function discussed in the video?

• All real numbers except zero.

• All real numbers.

• Only positive numbers.

• Only negative numbers.