Understanding Rational Functions

The video tutorial explains how to write an equation for a rational function based on its graph. It covers identifying key graph characteristics such as intercepts and vertical asymptotes, setting up the rational function in factored form, and solving for the constant 'a' using the intercepts. The tutorial concludes by finalizing the rational function and verifying its characteristics, including the horizontal asymptote.

What is the first step in writing an equation for a rational function based on its graph?

• Identifying the horizontal asymptotes

• Determining the degree of the function

• Finding the intercepts and vertical asymptotes

• Calculating the slope of the graph

What does a vertical asymptote at x = -4 indicate about the rational function?

• x - 4 is a factor in the denominator

• x - 4 is a factor in the numerator

• x + 4 is a factor in the numerator

• x + 4 is a factor in the denominator

How does an x-intercept of -2 affect the rational function's equation?

• It adds a factor of x + 2 in the denominator

• It adds a factor of x + 2 in the numerator

• It adds a factor of x - 2 in the denominator

• It adds a factor of x - 2 in the numerator

What is the role of the y-intercept in determining the rational function?

• It provides a factor for the numerator

• It helps find the degree of the function

• It determines the horizontal asymptote

• It is used to calculate the constant 'a'

What is the value of 'a' if the function passes through the point (0, -2)?

• 1

• 2

• 3

• 4

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

• 0

• 1

• 3

• 2

What is the degree of the denominator in the final rational function?

• 3

• 0

• 1

• 2

What is the horizontal asymptote of the rational function?

• y = -1

• y = 2

• y = 0

• y = 1

Which of the following is true about the rational function's graph?

• The degree of the numerator is greater than the denominator

• The degree of the numerator is equal to the denominator

• The degree of the numerator is less than the denominator

• The graph has no intercepts

What characteristic of the graph confirms the horizontal asymptote?

• The degree of the denominator

• The degree of the numerator

• The y-intercept

• The x-intercept