Function Operations and Properties

The video tutorial explains function arithmetic, covering addition, subtraction, multiplication, and division of functions f(x) and g(x). It demonstrates how to expand functions, combine like terms, and determine the domain for each operation. The tutorial emphasizes careful handling of subtraction and division, especially regarding domain restrictions due to division by zero.

What is the first step in performing function arithmetic when given f(x) in factored form?

• Determine the domain

• Expand the factored form

• Combine like terms

• Distribute negative signs

When adding two functions, what should you do after expanding and combining like terms?

• Determine the domain

• Simplify the coefficients

• Distribute negative signs

• Factor the expression

In the subtraction of functions, why is it important to use parentheses around g(x)?

• To ensure correct addition

• To distribute the positive sign

• To subtract the entire function

• To simplify the expression

What is the result of combining like terms in the expression x^2 + 4x + 4 - (2 - 3x)?

• x^2 + 7x + 2

• x^2 + x + 6

• x^2 + 4x + 2

• x^2 + 3x + 4

How many products result from multiplying a trinomial by a binomial?

• Six

• Four

• Five

• Seven

What is the highest degree term in the product of f(x) and g(x)?

• x^3

• x^2

• x^4

• x^5

What is the domain of the product of two polynomial functions?

• All real numbers

• All positive numbers

• All negative numbers

• All integers

When dividing functions, why is it important to determine the domain?

• To factor the denominator

• To simplify the numerator

• To avoid division by zero

• To find the range

What value of x makes the denominator zero in the division of f(x) by g(x)?

• x = 4/5

• x = 3/4

• x = 2/3

• x = 1/2

What is the factored form of x^2 + 4x + 4?

• (x + 4)^2

• (x + 2)^2

• (x + 1)^2

• (x + 3)^2