Understanding Function Addition and Evaluation

The video tutorial explains how to add two quadratic functions, f(x) and g(x), by combining like terms. It demonstrates the process of finding f+g(x) and then calculating f+g(4) using two different methods: direct substitution and using the definition of f+g(x). The tutorial emphasizes the importance of parentheses in function operations and provides a step-by-step guide to ensure accuracy in calculations.

What is the first step in finding f + g(x) when given f(x) and g(x)?

• Multiply the functions together

• Add the functions by combining like terms

• Subtract g(x) from f(x)

• Divide f(x) by g(x)

When adding two quadratic functions, why is it important to clear the parentheses?

• To divide the functions accurately

• To simplify the multiplication

• To ensure correct addition of like terms

• To make subtraction easier

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

• 4x^2

• 3x^2

• 5x^2

• 2x^2

How do you find f + g(4) using the expression for f + g(x)?

• Substitute 4 for x in f + g(x)

• Substitute 4 for x in g(x) only

• Substitute 4 for x in f(x) only

• Multiply f(x) and g(x) at x = 4

What is the value of f + g(4) when calculated using the expression for f + g(x)?

• 30

• 25

• 20

• 35

In the alternative method, what is the first step to find f + g(4)?

• Multiply f(4) by g(4)

• Subtract g(4) from f(4)

• Divide f(4) by g(4)

• Evaluate f(4) and g(4) separately

What is the result of evaluating f(4) for f(x) = 3x^2 - 5x + 2?

• 50

• 52

• 48

• 42

What is the result of evaluating g(4) for g(x) = x^2 - 4x - 5?

• -5

• 0

• 10

• 5

What is the final result of f + g(4) using the alternative method?

• 35

• 30

• 25

• 20

Why is it beneficial to verify the result of f + g(4) using two different methods?

• To find multiple solutions

• To make the process more complex

• To ensure the result is consistent and accurate

• To practice different mathematical operations