Exploring Function Operations in Algebra 2

This video tutorial covers function operations, including addition, subtraction, multiplication, division, and composition of functions. It explains how to find the domain of resulting functions and provides examples for each operation. The tutorial also discusses the importance of factoring in division and the process of composing functions with examples.

What is the result of adding the functions f(x) = 3x + 4 and g(x) = x² - 5x + 2?

• x² + 2x + 6

• x² - 8x + 6

• x² - 2x + 6

• x² + 8x + 6

Tags

CCSS.HSF-BF.A.1B

When subtracting the function g(x) from f(x), what is the correct result?

• x² - 8x - 2

• x² + 8x + 2

• -x² - 8x + 2

• -x² + 8x + 2

Tags

CCSS.HSF-BF.A.1B

If the demand function is d(x) = 5000 - 10x and the price function is p(x) = x, what is the revenue function?

• 5000 - 10x

• 5000x + 10x²

• 5000x - x²

• 5000x - 10x²

Tags

CCSS.HSF-BF.A.1B

What is the result of dividing f(x) = x - 7 by g(x) = 2x² - 13x - 7 after factoring?

• 1 / (x - 7)

• x / (x - 7)

• x / (2x + 1)

• 1 / (2x + 1)

Tags

CCSS.HSA.APR.D.6

What are the domain restrictions when dividing f(x) by g(x)?

• x cannot be -7 and x cannot be -1/2

• x cannot be -7 and x cannot be 1/2

• x cannot be 7 and x cannot be 1/2

• x cannot be 7 and x cannot be -1/2

What is the result of the composition f(g(3)) if f(x) = x² and g(x) = x + 1?

• 4

• 9

• 1

• 16

Tags

CCSS.HSF-BF.A.1C

What is the general form of f(g(x)) if f(x) = x² and g(x) = x + 1?

• x² + x + 1

• x² - x + 1

• x² + 2x + 1

• x² - 2x + 1

Tags

CCSS.HSF-BF.A.1C

What is the first step in finding f(g(x)) for f(x) = x² and g(x) = x + 1?

• Square x

• Add x and 1

• Substitute x + 1 into f(x)

• Multiply x and 1

Tags

CCSS.HSF-BF.A.1C

What is the simplified form of f(g(x)) if f(x) = √(x + 7) and g(x) = 2x - 5?

• √(2x - 2)

• √(2x + 12)

• √(2x + 2)

• √(2x - 12)

Tags

CCSS.HSF-BF.A.1C

What is the result of f(g(x)) if f(x) = x² + x + 2 and g(x) = 4 - x?

• x² + 9x - 22

• x² - 9x - 22

• x² + 9x + 22

• x² - 9x + 22

Tags

CCSS.HSF-BF.A.1C