Quotient of two linear functions to determine the domain

The video tutorial explains how to divide two functions, F(x) and G(x), and the implications for the domain of the resulting function. It highlights that while addition, subtraction, and multiplication of functions do not affect the domain, division introduces a constraint because the denominator cannot be zero. The tutorial walks through the process of identifying this constraint, setting the denominator equal to zero, and determining the restricted domain. It concludes with instructions on how to graph the domain, emphasizing the use of parentheses to denote undefined points and the use of a union symbol to connect intervals.

What is the main difference between dividing functions and other operations like addition or multiplication?

• Division is only applicable to polynomial functions.

• Division requires considering the domain due to potential division by zero.

• Division is always more complex than addition or multiplication.

• Division results in a larger range of values.

When dividing 3x + 1 by x - 2, what constraint is introduced?

• The denominator cannot be zero.

• The result must be a whole number.

• The numerator must be greater than zero.

• The functions must be linear.

How do you determine the domain of a function after division?

• Include only positive numbers.

• Exclude the value that makes the denominator zero.

• Exclude negative numbers.

• Include all real numbers.

What is the domain of the function 3x + 1 divided by x - 2?

• All real numbers except 2.

• Only positive numbers.

• All real numbers except -2.

• All real numbers.

How is the domain expressed in interval notation for the function 3x + 1 divided by x - 2?

• (-∞, 2) ∪ (2, ∞)

• (-∞, -2) ∪ (-2, ∞)

• (-∞, 0) ∪ (0, ∞)

• (-∞, ∞)