Finding Domain and Range of Rational Functions

This tutorial explains how to find the domain and range of a rational function using various methods. It covers graphical and algebraic approaches for determining the domain, including identifying vertical asymptotes and setting the denominator to zero. For the range, the video explores graphical methods, algebraic manipulation, and the use of limits to identify horizontal asymptotes. The tutorial concludes with additional tips and emphasizes the importance of understanding these concepts for analyzing rational functions.

What is the main focus of this tutorial?

• Finding the domain and range of a rational function

• Solving quadratic equations

• Understanding polynomial roots

• Graphing linear functions

What is the given rational function in the tutorial?

• 3x - 1 divided by 2x + 5

• 2x + 3 divided by x - 5

• 5x + 1 divided by x - 3

• x^2 - 4 divided by x + 2

What does the domain of a function represent?

• The minimum value of the function

• The maximum value of the function

• The set of all possible x-values

• The set of all possible y-values

How is the vertical asymptote identified in the first method for finding the domain?

• By finding the x-intercepts

• By setting the denominator equal to zero

• By graphing the function and observing breaks

• By solving the numerator equal to zero

What is the value of x that cannot be included in the domain?

• x = 3/2

• x = 0

• x = 5/2

• x = -5/2

In the second method for finding the domain, what is done with the denominator?

• It is set equal to zero

• It is ignored

• It is multiplied by the numerator

• It is divided by the numerator

How can the domain be expressed in set notation?

• As a single number

• As a list of x-values excluding certain values

• As a graph

• As a list of y-values

What is the horizontal asymptote identified in the range?

• y = 0

• y = 3/2

• y = -5/2

• y = 5/2

In the first method for finding the range, what is the first step?

• Find the x-intercepts

• Set y equal to zero

• Make x the subject

• Graph the function

What is the result of solving for y in the first method for finding the range?

• y = 0

• y = 3/2

• y = -5/2

• y = 5/2