Adding and Subtracting Rational Expressions

This video tutorial covers the basics of rational functions, including their definition, graphing techniques, and the identification of vertical and horizontal asymptotes, as well as holes. It provides a step-by-step guide to graphing rational functions and explains how to use graphing calculators effectively. The tutorial also includes several example problems to reinforce the concepts discussed.

What is a rational function?

• A function that is always quadratic

• A function that can be written as a ratio of two polynomials

• A function that is always linear

• A function that has no asymptotes

What is an asymptote?

• A line that the graph approaches but never touches

• A point where the graph intersects the y-axis

• A line that the graph crosses

• A point where the graph intersects the x-axis

How is a hole in a rational function graph identified?

• By finding the degree of the numerator

• By finding the zeros of the denominator

• By finding the zeros of the numerator

• By finding common factors that cancel out in the numerator and denominator

What is the first step in graphing a rational function?

• Finding the vertical asymptotes

• Finding the x-intercepts

• Finding the y-intercepts

• Factoring and simplifying the function

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

• By finding the degree of the denominator

• By finding the degree of the numerator

• By setting the denominator equal to zero and solving

• By setting the numerator equal to zero and solving

What determines the horizontal asymptote when the degree of the numerator is less than the degree of the denominator?

• There is no horizontal asymptote

• The horizontal asymptote is the x-axis

• The horizontal asymptote is y = 0

• The horizontal asymptote is the leading coefficient of the numerator divided by the leading coefficient of the denominator

What is the domain of a rational function?

• All real numbers except where the denominator is zero

• All real numbers except where the numerator is zero

• All real numbers except where the function has a hole

• All real numbers except where the function is undefined

In the example where the function is simplified to x - 5, what type of function is it?

• Exponential function

• Quadratic function

• Rational function

• Linear function

What happens when a rational function has two vertical asymptotes?

• The graph will have no asymptotes

• The graph will have two separate hyperbolic curves

• The graph will be a straight line

• The graph will have a single hyperbolic curve

What is the range of a rational function with a horizontal asymptote at y = 2 and a y-intercept at 4.5?

• All y-values less than 2 and greater than 4.5

• All y-values greater than 2 and less than 4.5

• All y-values except y = 4.5

• All y-values except y = 2