Finding and graphing the vertical and horizontal asymptotes

The video tutorial explains how to find the domain of a rational function by identifying values that make the denominator zero. It discusses vertical asymptotes, which occur where the function is undefined, and horizontal asymptotes, determined by comparing the degrees of the polynomials. The tutorial provides a step-by-step approach to solving these problems and visualizing the asymptotes on a graph.

What is the domain of a rational function?

• All real numbers

• All values except those that make the denominator zero

• All values except those that make the numerator zero

• Only positive real numbers

How do you find the vertical asymptote of a rational function?

• Find the highest degree of the numerator

• Set the denominator equal to zero

• Find the highest degree of the denominator

• Set the numerator equal to zero

What does a vertical asymptote represent in a graph?

• A point where the graph crosses the y-axis

• A line where the graph approaches but never touches

• A line where the graph intersects

• A point where the graph crosses the x-axis

When the degrees of the numerator and denominator are equal, how is the horizontal asymptote found?

• By multiplying the coefficients

• By subtracting the coefficients

• By adding the coefficients

• By dividing the coefficients

What happens to the graph at a horizontal asymptote?

• The graph crosses the asymptote

• The graph approaches but never crosses the asymptote

• The graph intersects the asymptote

• The graph remains constant at the asymptote