Determine the vertical and oblique asymptotes

The video tutorial explains how to find vertical, horizontal, and slant asymptotes in rational functions. It begins with identifying vertical asymptotes by setting the denominator to zero. The absence of horizontal asymptotes is discussed when the degree of the numerator is greater than the denominator, leading to the need for slant asymptotes. The tutorial demonstrates using long division to find slant asymptotes, emphasizing the importance of understanding the process over synthetic division. The final slant asymptote is determined, and its role in graphing the function is highlighted.

What is the condition for a vertical asymptote in a rational function?

• The numerator equals zero.

• The degrees of numerator and denominator are equal.

• The function is undefined.

• The denominator equals zero.

When does a rational function have no horizontal asymptote?

• When the degree of the numerator is equal to the degree of the denominator.

• When the degree of the numerator is less than the degree of the denominator.

• When the function is a constant.

• When the degree of the numerator is greater than the degree of the denominator.

What method is used to find a slant asymptote when the degree of the numerator is greater than the degree of the denominator?

• Synthetic division

• Factoring

• Completing the square

• Long division

In the process of long division, what is the first step after setting up the division?

• Divide the leading terms.

• Subtract the rows.

• Add zeros for missing terms.

• Multiply the divisor by the quotient.

What is the significance of the remainder in finding a slant asymptote?

• It is used to find the horizontal asymptote.

• It determines the vertical asymptote.

• It is ignored in the final equation of the slant asymptote.

• It helps in finding the x-intercepts.