Understanding Rational Functions

The video tutorial explains how to analyze a rational function by determining its y-intercept, x-intercepts, vertical and horizontal asymptotes, and any possible holes. It emphasizes the importance of factoring the function to simplify it and identify common factors that lead to holes. The tutorial guides viewers through the process of simplifying the function, finding intercepts, and determining asymptotes, using both the original and simplified forms of the function. The video concludes with a verification of the results through graphing.

What is the first step in analyzing a rational function?

• Factoring the function

• Graphing the function

• Determining the asymptotes

• Finding the intercepts

What is the common factor in the numerator and denominator of the given function?

• 2X

• X + 2

• X - 4

• X + 3

What happens to the graph of the function at X = 4?

• It has an x-intercept

• It has a vertical asymptote

• It has a hole

• It has a horizontal asymptote

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

• Analyze the degree of the numerator

• Set Y equal to 0

• Set X equal to 0

• Find the common factor

What is the x-intercept of the simplified function?

• X = 0

• X = -3

• X = 2

• X = 4

Why is there no x-intercept at X = 4?

• Because the function is undefined at X = 4

• Because X = 4 is a vertical asymptote

• Because X = 4 is the y-intercept

• Because X = 4 is a horizontal asymptote

What is the equation of the vertical asymptote?

• X = 2

• X = 0

• X = -2

• X = 4

How is the horizontal asymptote determined when the degrees of the numerator and denominator are the same?

• By setting the numerator equal to zero

• By setting the denominator equal to zero

• By taking the ratio of the leading coefficients

• By finding the common factor

What is the horizontal asymptote of the function?

• Y = 2

• Y = 1

• Y = 1/2

• Y = 0

What does the graph verify about the function?

• The absence of a horizontal asymptote

• The presence of a hole at X = 4

• The absence of a y-intercept

• The presence of a vertical asymptote at X = 4