Factoring, Domains, and Function Operations

The video tutorial covers operations on functions, including addition, subtraction, multiplication, division, and composition. It explains how to find the domain for each operation, emphasizing the importance of considering original functions for domain constraints. The tutorial also highlights the use of parentheses in subtraction and division to avoid errors and discusses factoring in simplifying rational expressions.

What is the result of adding the functions f(x) = x^2 - 9 and g(x) = x + 3?

• x^2 + x + 6

• x^2 + x - 6

• x^2 - x + 6

• x^2 - x - 6

When combining like terms in the expression x^2 - 9 + x + 3, what is the constant term?

• 12

• -12

• 6

• -6

What is the domain of the function f(x) = x^2 - 9 + x + 3?

• All real numbers except x = 0

• All real numbers

• All real numbers except x = -3

• All real numbers except x = 3

Which of the following is a restriction when determining the domain of a function?

• Negative coefficients

• Terms with x^2

• Denominators equal to zero

• Positive constants

What is the result of multiplying the functions f(x) = x^2 - 9 and g(x) = x + 3 using the FOIL method?

• x^3 + 3x^2 + 9x + 27

• x^3 - 3x^2 + 9x + 27

• x^3 - 3x^2 - 9x - 27

• x^3 + 3x^2 - 9x - 27

What is the domain of the product of the functions f(x) = x^2 - 9 and g(x) = x + 3?

• All real numbers except x = -3

• All real numbers

• All real numbers except x = 0

• All real numbers except x = 3

What is the result of dividing the functions f(x) = x^2 - 9 by g(x) = x + 3?

• x^2 - 3

• x^2 + 3

• x + 3

• x - 3

When dividing functions, why is it important to consider the original function for domain restrictions?

• To determine the degree of the polynomial

• To find the range

• To identify potential holes

• To simplify the expression

What is the domain of the function f(x) = (x^2 - 9) / (x + 3)?

• All real numbers except x = 0

• All real numbers

• All real numbers except x = -3

• All real numbers except x = 3

What value of x makes the denominator zero in the function f(x) = (x^2 - 9) / (x + 3)?

• 0

• -3

• 9

• 3