How do you find the vertical and horizontal asymptotes of a rational function

The video tutorial explains the concepts of reciprocal and rational functions, focusing on asymptotes. It covers vertical and horizontal asymptotes, detailing how they are determined by the degrees of polynomials and leading coefficients. The tutorial provides examples to illustrate these concepts, ensuring a comprehensive understanding of how asymptotes affect graph behavior.

What is the main reason a graph of a reciprocal function never touches the line x = 0?

• Because it is a vertical line

• Because it is a horizontal line

• Because division by zero is undefined

• Because it is a diagonal line

In a rational function, what determines the location of a vertical asymptote?

• The denominator equals zero

• The numerator is greater than the denominator

• The numerator is less than the denominator

• The numerator equals zero

When the degree of the denominator is greater than the degree of the numerator, what is the horizontal asymptote?

• x = 1

• y = 1

• x = 0

• y = 0

If the degree of the numerator is greater than the degree of the denominator, what is the horizontal asymptote?

• y = 0

• There is no horizontal asymptote

• y = 1

• x = 0

What happens when the degrees of the numerator and denominator are equal in a rational function?

• The vertical asymptote is determined by the leading coefficients

• The horizontal asymptote is determined by the leading coefficients

• There is no horizontal asymptote

• The horizontal asymptote is y = 0

What is the leading coefficient of the polynomial 4x^2 + 2x - 1?

• 4

• 1

• 0

• 2

How do you find the horizontal asymptote when the degrees of the numerator and denominator are equal?

• By setting the numerator equal to zero

• By adding the leading coefficients

• By setting the denominator equal to zero

• By dividing the leading coefficients

What is the degree of the polynomial 3x^4 - 5x^2 + 2x^8?

• 4

• 2

• 8

• 5

What is the horizontal asymptote of a rational function where the leading coefficient of the numerator is 4 and the leading coefficient of the denominator is -5?

• y = 0

• y = 4/-5

• y = -5

• y = 4

What is the first step in finding vertical asymptotes of a rational function?

• Find the leading coefficient

• Set the denominator equal to zero

• Find the degree of the numerator

• Set the numerator equal to zero