Evaluating Functions and Function Notation

The video tutorial explains how to evaluate functions by substituting values into equations. It covers four examples: evaluating f(2) using PEMDAS, finding G(-3) with substitution, evaluating f(x+h) through distribution and simplification, and solving for x when M(x) equals 6 using algebra. The tutorial emphasizes careful handling of parentheses and order of operations.

What is the independent variable in a function?

• The output value

• The dependent variable

• The input value

• The y-value

What is the output value in a function?

• The input value

• The x-value

• The independent variable

• The y-value

In the function f(x) = x^2 - 3x + 1, what is f(2)?

• 5

• 3

• 7

• 1

What is the importance of the order of operations in evaluating functions?

• It helps in simplifying the function

• It makes the function look neat

• It ensures the correct result

• It avoids negative values

Why is it important to use parentheses when substituting values into functions?

• To simplify the function

• To avoid negative values

• To ensure correct order of operations

• To make the function look neat

What is G(-3) if G(x) = -5x - 10?

• 5

• -25

• -5

• 15

When evaluating f(x + h) for f(x) = 4x^2 - x, what is the first step?

• Distribute the negative sign

• Combine like terms

• Replace x with x + h

• Simplify the expression

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

• 4x^2 + 8xh + 4h^2 - x + h

• 4x^2 + 4xh + 4h^2 - x + h

• 4x^2 + 8xh + 4h^2 - x - h

• 4x^2 + 4xh + 4h^2 - x - h

What is the final result of f(x + h) for f(x) = 4x^2 - x?

• 4x^2 + 4xh + 4h^2 - x - h

• 4x^2 + 8xh + 4h^2 - x - h

• 4x^2 + 4xh + 4h^2 - x + h

• 4x^2 + 8xh + 4h^2 - x + h

If M(x) = x^2 - 3 and M(x) = 6, what is x?

• 3

• 0

• -3

• ±3