Exploring Function Operations and Compositions

The video tutorial covers key concepts of adding, subtracting, multiplying, and composing functions. It begins with an introduction to these operations, comparing them to polynomial operations. The instructor provides examples for each operation, demonstrating how to combine functions and calculate their domain and range. The tutorial also includes a detailed explanation of function composition, using specific examples to illustrate the process. Throughout the video, the instructor emphasizes understanding the properties of linear and cubic functions.

What are the key concepts covered in today's lesson?

• Only adding and subtracting functions

• Only multiplying and dividing functions

• Adding, subtracting, and dividing functions

• Adding, subtracting, and multiplying functions

What is the result of adding f(x) = 4x + 7 and g(x) = 12 + x?

• 5x + 12

• 4x + 12

• 4x + 19

• 5x + 19

What is the domain of the function resulting from f(x) - g(x) where f(x) = 4x + 7 and g(x) = 12 + x?

• Negative infinity to positive infinity

• 0 to positive infinity

• Negative infinity to 0

• 0 to 10

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

• 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 type of function is the result of multiplying f(x) = x^2 - 9 and g(x) = x + 3?

• Linear

• Quadratic

• Exponential

• Cubic

What is the domain of the cubic function resulting from f(x) * g(x)?

• Negative infinity to 0

• Negative infinity to positive infinity

• 0 to 10

• 0 to positive infinity

What tool is used to visualize the functions in the lesson?

• Mathematica

• Desmos

• Graphing calculator

• Excel

What is the first step in composing the functions f(x) = x - 5 and g(x) = x^2 for g(f(-3))?

• Evaluate g(x)

• Evaluate g(-3)

• Evaluate f(-3)

• Evaluate f(x)

What is the result of f(-3) when f(x) = x - 5?

• 2

• 8

• -8

• -2

What is the final result of g(f(-3)) when f(x) = x - 5 and g(x) = x^2?

• 25

• 49

• 81

• 64