Understanding Rational Functions

The video tutorial explains how to analyze and graph rational functions. It begins with factoring the numerator and denominator, then discusses the domain, vertical asymptotes, and intercepts. The tutorial also covers horizontal asymptotes by examining the degrees of the numerator and denominator. Finally, it demonstrates graphing the function using these components, emphasizing the importance of asymptotes and intercepts.

What is the first step in analyzing a rational function?

• Graphing the function

• Finding the domain

• Factoring the numerator and denominator

• Identifying intercepts

Why is x = -2 excluded from the domain of the function?

• It is a vertical intercept

• It is a horizontal asymptote

• It is a zero of the denominator

• It is a zero of the numerator

What results in a vertical asymptote in a rational function?

• Zeros of the numerator

• Zeros of the denominator

• Intercepts

• Common factors

What is the horizontal intercept of the function?

• (0, 2)

• (4, 0)

• (-2, 0)

• (0, -2)

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

• Find common factors

• Analyze end behavior

• Set y to zero

• Set x to zero

What determines the horizontal asymptote of a rational function?

• The degree of the numerator

• The degree of the denominator

• The ratio of leading coefficients

• The zeros of the numerator

What is the equation of the horizontal asymptote in this function?

• y = 1

• y = -1

• y = 2

• y = 0

Which tool is used to graph a rational function in an online system?

• Graphing calculator

• Graphing tool

• Spreadsheet

• Drawing software

What symmetry is used to graph the second piece of the function?

• Bilateral symmetry

• Translational symmetry

• Rotational symmetry

• Reflective symmetry

What point is used to demonstrate rotational symmetry in the graph?

• (-4, -4)

• (4, 0)

• (0, 2)

• (-2, -1)