Exploring Function Operations in Algebra 2

The video tutorial covers various operations on functions, including addition, subtraction, multiplication, division, and composition. It emphasizes understanding the domains of resulting functions and provides examples for each operation. The tutorial also discusses how to handle domain constraints in real-world contexts, particularly for multiplication and division. Finally, it explains function composition and how to evaluate and create new functions through composition.

What is the main focus of the video tutorial?

• Discussing the limitations of functions

• Exploring the applications of functions in real life

• Learning about function operations and their domains

• Understanding the history of functions

When adding two functions, what is the resulting function of f(x) = x^2 - 2x + 6 and g(x) = x^2 - 5x + 2?

• 2x^2 - 7x + 8

• x^2 - 7x + 8

• 2x^2 - 7x + 4

• x^2 - 7x + 4

What happens to the signs of the second function when subtracting f(x) - g(x)?

• They become zero

• They double

• They change to the opposite sign

• They remain the same

What is the domain of the sum and difference of two functions if both original functions have domains of all real numbers?

• All real numbers

• Non-zero real numbers

• Positive real numbers

• Negative real numbers

In the context of word problems, what must be true about the price and demand functions?

• Both price and demand must be positive

• Both price and demand must be negative

• Price must be positive and demand must be negative

• Price must be negative and demand must be positive

What is the domain of the resulting function when multiplying P(x) = x and D(x) = 5000 - 10x?

• 0 ≤ x ≤ 500

• x > 500

• x = 0

• x < 0

When dividing functions, what must be true about the denominator?

• It must be a positive integer

• It cannot equal zero

• It must be less than zero

• It must be greater than zero

What is the result of dividing f(x) = x - 7 by g(x) = 2x^2 - 13x - 7 after factoring?

• 1 / (2x + 1)

• x / (x + 7)

• x / (2x + 1)

• 1 / (x + 7)

How is the composition of functions written?

• f(x) * g(x)

• f(x) + g(x)

• f(x) - g(x)

• f(g(x)) or g(f(x))

What is the result of the composition f(g(5)) if f(x) = x^2 and g(x) = x + 1?

• 25

• 30

• 36

• 26