How to graph a rational function by simplifying to the reciprocal functions

The video tutorial covers the concepts of horizontal and vertical asymptotes, explaining how to determine them by comparing polynomial degrees and coefficients. It also discusses finding X and Y intercepts, emphasizing the importance of setting the numerator to zero for X intercepts. The tutorial further explores the domain and range of functions, suggesting graphing as a method to verify range. Finally, it introduces long division and mixed numbers, demonstrating how to represent rational functions in different forms.

How do you determine the horizontal asymptote of a rational function when the degrees of the numerator and denominator are the same?

• By subtracting the leading coefficients

• By adding the leading coefficients

• By multiplying the leading coefficients

• By dividing the leading coefficients

What condition must be met for a vertical asymptote to occur in a rational function?

• The numerator must be zero

• The denominator must be zero

• The degrees of numerator and denominator must be equal

• The leading coefficients must be equal

How can you find the X intercept of a rational function?

• Set both numerator and denominator to zero

• Set the numerator to zero

• Set the denominator to zero

• Set X to one

What is the Y intercept of a rational function when X is zero?

• The value of the function at X equals zero

• The ratio of the numerator to the denominator

• The value of the numerator

• The value of the denominator

What is the domain of a rational function?

• All real numbers

• All real numbers except where the denominator is zero

• All real numbers except where the numerator is zero

• All positive real numbers

How can long division help in understanding the behavior of a rational function?

• It simplifies the function to a polynomial

• It converts the function to a mixed number form

• It changes the function to a linear form

• It eliminates the asymptotes

What is the range of a rational function with a horizontal asymptote at y = 3?

• All negative real numbers

• All real numbers

• All real numbers except y = 3

• All positive real numbers