Analyzing Rational Functions Concepts

The video tutorial explains how to analyze and graph a rational function. It covers factoring the numerator and denominator, determining the domain by excluding zeros of the denominator, identifying vertical and horizontal asymptotes, and finding intercepts. The tutorial also demonstrates how to graph the function using these components, emphasizing the importance of understanding end behavior and symmetry.

What is the first step in analyzing a rational function?

• Factor the numerator and denominator

• Find the vertical intercept

• Identify the holes

• Determine the horizontal asymptote

Why is positive two excluded from the domain of the function?

• It is an asymptote

• It is a common factor

• It is a zero of the denominator

• It is a zero of the numerator

What results in holes in the graph of a rational function?

• Zeros of the numerator

• Vertical asymptotes

• Zeros of the denominator

• Common factors between numerator and denominator

What is the equation of the vertical asymptote for the given function?

• x = -1

• x = 1

• x = 0

• x = 2

How do you find the horizontal intercept of a rational function?

• Set the numerator to zero

• Evaluate the function at x=0

• Find the common factors

• Set the denominator to zero

What is the vertical intercept of the function?

• (-1, 0)

• (1, 0)

• (0, -1)

• (0, 1)

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

• By the sum of the coefficients

• By the product of the coefficients

• By the ratio of the leading coefficients

• By the difference of the degrees

What is the horizontal asymptote of the function?

• y = 2

• y = 0

• y = 1

• y = -2

Which point is used to determine the second piece of the graph using symmetry?

• (-1, 0)

• (4, -5)

• (2, -2)

• (0, 1)

What is the purpose of using rotational symmetry in graphing the function?

• To find the vertical asymptote

• To determine the domain

• To locate additional points on the graph

• To calculate the horizontal intercept