Understanding Graphing of Rational Functions

This video tutorial covers the fundamentals of graphing rational functions, including understanding the components of rational functions, identifying restrictions such as vertical asymptotes and holes, and the steps to accurately graph these functions. It provides examples and practice problems to reinforce learning and explains how to analyze graphs for key features like asymptotes and intercepts. The tutorial concludes with methods for writing equations based on given graphs.

What is the domain of a rational function?

• All real numbers except where the numerator is zero

• All integers

• All real numbers

• All real numbers except where the denominator is zero

What is a vertical asymptote in a rational function?

• A line the graph will never cross

• A point where the graph is continuous

• A line the graph will always cross

• A point where the graph crosses the x-axis

How do you find a hole in a rational function?

• By finding the highest degree term

• By finding a factor that cancels in both the numerator and denominator

• By finding where the denominator is zero

• By finding where the numerator is zero

What determines the horizontal asymptote of a rational function?

• The degree of the numerator compared to the degree of the denominator

• The y-intercept

• The sum of the coefficients

• The x-intercept

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

• Find the highest degree term

• Set both numerator and denominator equal to zero

• Set the numerator equal to zero

• Set the denominator equal to zero

What is the first step in graphing a rational function?

• Drawing the graph

• Plotting the y-intercept

• Factoring the numerator and denominator

• Finding the horizontal asymptote

When graphing, what does a dashed line represent?

• A vertical asymptote

• A y-intercept

• An x-intercept

• A hole

What happens to the graph of a rational function at a hole?

• The graph is continuous

• The graph crosses the y-axis

• The graph is undefined at that point

• The graph crosses the x-axis

How can you identify a cubic graph in rational functions?

• By having one vertical asymptote

• By having two vertical asymptotes

• By having a horizontal asymptote

• By having no vertical asymptotes

What is the significance of the leading coefficient in determining the horizontal asymptote?

• It determines the y-intercept

• It determines the vertical asymptote

• It determines the x-intercept

• It is used when the degrees of the numerator and denominator are equal