Domain and Range of Functions

The video tutorial explains how to find the domain and range of rational functions. It covers the basic concepts and provides detailed examples, including simple, linear, and complex rational functions. The tutorial also discusses the use of horizontal asymptotes and inverse functions to determine the range. Each example is broken down step-by-step, showing how to find the domain by setting the denominator not equal to zero and how to find the range by rewriting the function in terms of y.

How can the range of a rational function be found?

• By finding the domain of the inverse function

• By finding the vertical asymptote

• By finding the x-intercept

• By finding the y-intercept

What is the domain of a rational function?

• All negative numbers

• All positive numbers

• All real numbers except where the denominator is zero

• All real numbers

In Example 1, what is the domain of f(x) = 3/(x-2)?

• All real numbers except 2

• All real numbers

• All real numbers except -2

• All real numbers except 0

In Example 1, what is the range of f(x) = 3/(x-2)?

• All real numbers except 0

• All real numbers

• All real numbers except -3

• All real numbers except 3

In Example 2, what is the domain of f(x) = (3x+2)/(x+5)?

• All real numbers

• All real numbers except 5

• All real numbers except -5

• All real numbers except 0

In Example 2, what is the range of f(x) = (3x+2)/(x+5)?

• All real numbers except -3

• All real numbers except 0

• All real numbers except 3

• All real numbers

In Example 3, what is the domain of f(x) = (x-4)/(3x+5)?

• All real numbers

• All real numbers except 5/3

• All real numbers except 0

• All real numbers except -5/3

In Example 3, what is the range of f(x) = (x-4)/(3x+5)?

• All real numbers except -1/3

• All real numbers

• All real numbers except 0

• All real numbers except 1/3

In Example 4, what is the domain of f(x) = (x-3)/(x^2-9)?

• All real numbers

• All real numbers except 3 and -3

• All real numbers except 9

• All real numbers except 0

In Example 4, what is the range of f(x) = (x-3)/(x^2-9)?

• All real numbers except 3

• All real numbers except 0

• All real numbers except -3

• All real numbers