Understanding Rational Functions

The video tutorial guides viewers through determining a rational function for a given graph. It begins by identifying vertical and horizontal asymptotes and intercepts. The function is constructed using these factors, and the constant 'a' is calculated based on the horizontal asymptote. The function is verified by checking a point on the graph, ensuring accuracy. The tutorial concludes with a summary of the process.

What are the vertical asymptotes of the given graph?

• x = -4 and x = 3

• x = 0 and x = 2

• y = 2

• x = 1 and x = 5

Which of the following is the horizontal asymptote of the graph?

• y = 0

• x = 0

• x = 2

• y = 2

What factors must the denominator include based on the vertical asymptotes?

• (x + 4) and (x - 3)

• (x - 4) and (x + 3)

• (x + 2) and (x - 2)

• (x - 1) and (x + 1)

Which factors should be included in the numerator based on the horizontal intercepts?

• (x + 4) and (x - 3)

• (x - 1) and (x + 1)

• x and (x + 2)

• x and (x - 2)

How do you determine the constant 'a' in the rational function?

• By analyzing the vertical asymptotes

• By using the point (4, 2)

• By comparing the degrees of the numerator and denominator

• By checking the horizontal intercepts

What is the degree of the numerator in the rational function?

• 3

• 1

• 4

• 2

What is the ratio of the leading coefficients in the rational function?

• 4

• 2

• 1

• 3

Which point is used to verify the correctness of the rational function?

• (0, 0)

• (2, 0)

• (4, 2)

• (3, 1)

What is the value of f(4) in the rational function?

• 1

• 2

• 4

• 3

Why is it important to verify the function with a point on the graph?

• To determine the horizontal intercepts

• To find the vertical asymptotes

• To ensure the graph is drawn correctly

• To confirm the function satisfies the equation