Asymptotes and End Behavior Analysis

This video tutorial covers rational functions, focusing on their properties such as vertical and horizontal asymptotes. It explains how to calculate end behavior using polynomial degrees, with specific rules for bottom heavy, same heavy, and top heavy functions. The video also discusses slant asymptotes and provides practice problems for better understanding.

What is a rational function?

• A function that divides two polynomials

• A function with no polynomials

• A function that multiplies two polynomials

• A function with a single polynomial

What are vertical and horizontal asymptotes?

• Points where the graph intersects the axes

• Invisible lines that the graph approaches but never touches

• Curves that the graph follows

• Visible lines that the graph will cross

How do you determine end behavior from a graph?

• By looking at the x-intercepts

• By observing the y-values as x approaches infinity

• By counting the number of peaks

• By checking the symmetry of the graph

What happens to the function if the degree of the denominator is higher than the numerator?

• The function is top-heavy

• The function is bottom-heavy

• The function is same-heavy

• The function has no asymptotes

What is the limit of a bottom-heavy function as x approaches infinity?

• Undefined

• Zero

• The leading coefficient

• Infinity

What is the horizontal asymptote of a same-heavy function?

• Infinity

• The ratio of the leading coefficients

• Undefined

• Zero

What is the horizontal asymptote of a function with equal degrees in the numerator and denominator?

• Undefined

• Zero

• Infinity

• The ratio of the leading coefficients

What is the limit of a same-heavy function as x approaches infinity?

• Zero

• Infinity

• The ratio of the leading coefficients

• Undefined

What is the end behavior of a bottom-heavy function as x approaches negative infinity?

• Positive infinity

• Zero

• Negative infinity

• Undefined

What is the end behavior of a top-heavy function as x approaches positive infinity?

• Negative infinity

• Zero

• The leading coefficient

• Positive infinity