Graphing Rational Functions and Discontinuities

The video tutorial explains how to graph a rational function by first identifying discontinuities through factoring. It covers simplification of the function, identifying restrictions, and graphing with vertical asymptotes and holes. The tutorial also discusses the end behavior of the function and provides a step-by-step guide to sketching the graph, emphasizing the importance of understanding the behavior near vertical asymptotes.

What is the first step in graphing a rational function?

• Finding the x-intercepts

• Identifying the y-intercepts

• Finding discontinuities

• Calculating the slope

Why is it important to factor the rational function?

• To find the y-intercept

• To identify discontinuities

• To determine the slope

• To simplify the numerator

What does a common factor in the numerator and denominator indicate?

• A point of intersection

• A horizontal asymptote

• A hole in the graph

• A vertical asymptote

What is the simplified form of the given rational function?

• 1 over (x + 3)

• x over (x - 2)

• x squared over (x cubed)

• 2x over (x + 1)

Where are the holes located in the graph of the function?

• At x = -3 and x = 0

• At x = 0 and x = 2

• At x = 2 and x = -3

• At x = 1 and x = -1

What happens to the function as x approaches positive infinity?

• It approaches 0

• It approaches 1

• It approaches negative infinity

• It remains constant

What is the domain of the function after simplification?

• All real numbers except x = 3, -2

• All real numbers

• All real numbers except x = 0, 2, -3

• All real numbers except x = 1, -1