Rational Functions: Asymptotes and Intercepts

The video tutorial focuses on graphing advanced rational functions, starting with identifying horizontal and vertical asymptotes, and holes. It provides examples of factoring functions to find asymptotes and holes, and demonstrates graphing these functions while determining their domain and range. The tutorial also covers slant asymptotes and provides multiple example problems to illustrate these concepts.

What is the horizontal asymptote of a rational function where the degree of the denominator is greater than the numerator?

• y = 1

• x = 0

• y = 0

• x = 1

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

• Set the denominator equal to zero

• Find the y-intercept

• Find the x-intercept

• Set the numerator equal to zero

What is the domain of a rational function with a hole at x = -2 and a vertical asymptote at x = 3?

• (-∞, -2) ∪ (-2, 3) ∪ (3, ∞)

• (-∞, ∞)

• (-∞, -2) ∪ (3, ∞)

• (-∞, 3) ∪ (3, ∞)

What is the range of a rational function with a horizontal asymptote at y = 0 and a hole at y = -1/5?

• (-∞, -1/5) ∪ (0, ∞)

• (-∞, -1/5) ∪ (-1/5, 0) ∪ (0, ∞)

• (-∞, ∞)

• (-∞, 0) ∪ (0, ∞)

How do you determine the x-intercept of a rational function?

• Find the horizontal asymptote

• Find the vertical asymptote

• Set x equal to zero and solve for y

• Set y equal to zero and solve for x

What is the slant asymptote of a rational function where the degree of the numerator is one more than the denominator?

• It is the same as the horizontal asymptote

• It is the remainder from long division

• It is the quotient from long division

• There is no slant asymptote

How do you find the y-intercept of a rational function?

• Set y equal to zero and solve for x

• Set x equal to zero and solve for y

• Find the horizontal asymptote

• Find the vertical asymptote

What is the domain of a rational function with a vertical asymptote at x = 3?

• (-∞, ∞)

• (-∞, 0) ∪ (0, ∞)

• (-∞, 3) ∪ (3, ∞)

• (-∞, 3)

What is the range of a rational function with a horizontal asymptote at y = 2?

• (-∞, 2) ∪ (2, ∞)

• (-∞, ∞)

• (-∞, 0) ∪ (0, ∞)

• (-∞, 1) ∪ (1, ∞)

Why might a graphing calculator be useful when determining the range of a rational function?

• To find exact values of maximum and minimum y-values

• To find the x-intercepts

• To determine the horizontal asymptote

• To calculate the domain