Operations with Functions

This video tutorial from Howard Community College explains how to find the sum, difference, product, and quotient of two functions. It covers the process of combining functions and determining their domains, with a focus on ensuring no division by zero occurs in the quotient. The video provides step-by-step instructions and examples for each operation, emphasizing the importance of understanding domain restrictions.

What is the main topic discussed in the video?

• Graphing linear equations

• Finding the sum, difference, product, and quotient of two functions

• Solving systems of equations

• How to solve quadratic equations

What is the first step in finding the sum of two functions?

• Multiply the functions

• Subtract the functions

• Rewrite the sum as f(x) + g(x)

• Divide the functions

What is the result of combining like terms in the sum of f(x) = 3x^2 + 4 and g(x) = x - 5?

• 3x^2 + x - 1

• 3x^3 + x - 1

• 3x^2 + 4x - 5

• 3x^2 - x + 9

What is the domain of the sum of the functions f(x) = 3x^2 + 4 and g(x) = x - 5?

• x > 0

• x ≠ 5

• x < 0

• All real numbers

What is the first step in finding the difference of two functions?

• Divide the functions

• Rewrite the difference as f(x) - g(x)

• Add the functions

• Multiply the functions

What is the result of distributing the negative sign in the difference of f(x) = 3x^2 + 4 and g(x) = x - 5?

• 3x^2 - x + 9

• 3x^2 - x - 1

• 3x^2 + 4 + x - 5

• 3x^2 + x + 9

What is the domain of the difference of the functions f(x) = 3x^2 + 4 and g(x) = x - 5?

• x > 0

• x < 0

• x ≠ 5

• All real numbers

What is the first step in finding the product of two functions?

• Add the functions

• Divide the functions

• Multiply the functions

• Subtract the functions

What is the result of multiplying f(x) = 3x^2 + 4 and g(x) = x - 5?

• 3x^2 - x + 9

• 3x^3 - 15x^2 + 4x - 20

• 3x^3 + x - 1

• 3x^2 + x - 1

What is the domain of the product of the functions f(x) = 3x^2 + 4 and g(x) = x - 5?

• x < 0

• x ≠ 5

• x > 0

• All real numbers