Operations and Properties of Functions

The video tutorial explains how to perform operations on functions, including addition, subtraction, multiplication, and division. It covers the domains of these operations, emphasizing the importance of understanding the intersection of domains and handling cases where the denominator cannot be zero. The tutorial uses examples with quadratic and linear functions to illustrate these concepts, providing a comprehensive understanding of function operations and their domains.

What are the operations to be performed on the functions F(x) and G(x)?

• Addition, Subtraction, Multiplication, Division

• Addition, Subtraction, Exponentiation, Division

• Multiplication, Division, Modulus, Addition

• Subtraction, Division, Exponentiation, Multiplication

What is the result of adding F(x) = x^2 - 3x and G(x) = x + 6?

• x^2 - 2x + 6

• x^2 - 4x + 6

• x^2 + 3x + 6

• x^2 - 3x + 6

What is the domain of the sum of F(x) and G(x)?

• All positive numbers

• All integers

• All real numbers

• All negative numbers

What is the result of subtracting G(x) from F(x)?

• x^2 - 4x - 6

• x^2 - x - 6

• x^2 - 2x - 6

• x^2 - 3x - 6

What is the domain of the difference of F(x) and G(x)?

• All negative numbers

• All integers

• All real numbers

• All positive numbers

What is the result of multiplying F(x) and G(x)?

• x^3 + 6x^2 - 18x

• x^3 - 6x^2 + 18x

• x^3 - 3x^2 + 18x

• x^3 + 3x^2 - 18x

What is the domain of the product of F(x) and G(x)?

• All real numbers

• All positive numbers

• All negative numbers

• All integers

What is the expression for F(x) divided by G(x)?

• (x^2 - 3x) / (x - 6)

• (x^2 + 3x) / (x - 6)

• (x^2 - 3x) / (x + 6)

• (x^2 + 3x) / (x + 6)

What value must be excluded from the domain of the quotient of F(x) and G(x)?

• x = 3

• x = 0

• x = 6

• x = -6

What is the domain of the quotient of F(x) and G(x) in interval notation?

• (-∞, -6) U (-6, ∞)

• (-∞, 6) U (6, ∞)

• (-∞, 0) U (0, ∞)

• (-∞, 3) U (3, ∞)