Operations and Composition of Functions

Lesson 6.3 covers operations on functions, including addition, subtraction, multiplication, and division. It explains power functions and compositions, focusing on understanding domains and restrictions. The lesson provides examples and practice problems to reinforce learning.

What is the main focus of Lesson 6.3?

• Solving quadratic equations

• Graphing linear equations

• Understanding trigonometric identities

• Performing operations with various functions

Which of the following is an example of a power function?

• y = 3x + 4

• y = 3x^4

• y = 3/x

• y = log(x)

In the composition of functions, what is the result of G(f(x)) called?

• G(x)

• J(x)

• H(x)

• F(x)

What is the domain of a function?

• The set of all possible outputs

• The set of all possible inputs

• The inverse of the function

• The range of the function

Which operation is NOT one of the four basic operations on functions?

• Subtraction

• Exponentiation

• Division

• Addition

When adding two functions, what is the result of f(x) + g(x) if f(x) = 3x and g(x) = x + 3?

• 3x + x

• 3x + 3

• 6x + 3

• 4x + 3

Why can't we divide by zero in function operations?

• It results in a complex number

• It results in an undefined value

• It results in a positive value

• It results in a negative value

What is the domain of the function f(x) = 3x^1/2?

• All negative numbers

• All positive numbers

• All non-negative numbers

• All real numbers

In a composition of functions, if f(x) is not defined for a certain x, what can be said about g(f(x))?

• It is always defined

• It is defined for negative x only

• It is defined for all x

• It is not defined for that x

What happens to the domain of f/g if g(x) = 0 for some x?

• The domain is all positive numbers

• The domain is all real numbers

• The domain excludes that x

• The domain includes that x