Function Composition and Evaluation

The video tutorial explains the concept of function compositions, starting with a basic function that adds three to its input. It then explores applying this function multiple times and introduces a new function that quadruples its input. The tutorial demonstrates how the order of function application affects the result and provides examples of complex compositions involving multiple functions. The video concludes with a summary of how compositions of functions work.

What is the primary focus of the video tutorial?

• Basic arithmetic operations

• Graphing functions

• Solving equations

• Compositions of functions

What does the function f(x) = x + 3 do to an input x?

• Multiplies x by 3

• Divides x by 3

• Adds 3 to x

• Subtracts 3 from x

If f(x) = x + 3, what is f(2)?

• 5

• 6

• 4

• 3

What is the result of applying f(f(2))?

• 5

• 8

• 6

• 7

What is the result of f(f(x)) in terms of x?

• x + 6

• x + 3

• 2x + 3

• 2x + 6

What is the result of applying f to an input of 5?

• 7

• 8

• 9

• 10

What is the result of f(f(f(1)))?

• 6

• 9

• 7

• 8

What does the function g(x) = 4x do to an input x?

• Subtracts 4 from x

• Adds 4 to x

• Divides x by 4

• Multiplies x by 4

If g(x) = 4x, what is g(2)?

• 6

• 8

• 10

• 12

What is the result of applying g to an input of 3?

• 12

• 11

• 10

• 9