Determine the horizontal asymptotes

The video tutorial reviews rational functions, focusing on finding vertical and horizontal asymptotes. It explains the importance of polynomial degrees and how they determine the horizontal asymptote. The tutorial covers three scenarios: when the degree of the numerator is less than, equal to, or greater than the degree of the denominator. It also discusses the behavior of graphs in relation to horizontal asymptotes, emphasizing that the graph approaches the asymptote as it moves towards infinity.

What is the primary focus when dealing with rational functions in this lesson?

• Finding the roots of polynomials

• Solving quadratic equations

• Identifying vertical and horizontal asymptotes

• Graphing linear functions

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

• y = x

• No horizontal asymptote

• y = 0

• y = 1

If the degrees of the numerator and denominator are equal, how is the horizontal asymptote determined?

• By multiplying the leading coefficients

• By dividing the leading coefficients

• By adding the degrees

• By subtracting the degrees

What happens to the horizontal asymptote when the degree of the numerator is greater than the degree of the denominator?

• There is no horizontal asymptote

• The horizontal asymptote is y = x

• The horizontal asymptote is y = 1

• The horizontal asymptote is y = 0

What does a horizontal asymptote represent in the context of a graph?

• The maximum value of the graph

• The line the graph approaches as x approaches infinity or negative infinity

• The point where the graph intersects the y-axis

• The slope of the tangent line at a point