Function Notation and Simplification

The video tutorial explains how to use function notation with variables, focusing on substituting different expressions into functions and simplifying the results. It covers both simple and complex substitutions, including using binomials and handling subtraction of functions. The tutorial concludes with an example using a different function, G, to demonstrate the application of these concepts.

What are the two functions introduced in the video?

• m(x) and n(x)

• p(x) and q(x)

• h(x) and j(x)

• f(x) and g(x)

What is the main focus of the video tutorial?

• Graphing functions

• Using function notation with variables

• Solving quadratic equations

• Finding derivatives

What is the result of substituting 'a' into f(x)?

• a + 3

• a^2 - 3

• a^2 + 3

• a - 3

What is the result of substituting 'a' into f(x)?

• a - 3

• a^2 - 3

• a + 3

• a^2 + 3

What method is used to simplify (a + 1)^2?

• Substitution

• Quadratic formula

• FOIL method

• Distributive property

What is the simplified form of f(a + 1)?

• a^2 + 2a - 2

• a^2 + 1

• a^2 + 2a - 3

• a^2 + 2a + 1

What happens to the constant term when substituting 'a + 1' into f(x)?

• It remains unchanged

• It is squared

• It is doubled

• It is added to the variable

What is the role of the FOIL method in the video?

• To simplify binomial expressions

• To solve linear equations

• To find derivatives

• To graph functions

What is the simplified form of f(a + 1)?

• a^2 + 2a - 2

• a^2 + 2a + 1

• a^2 + 1

• a^2 + 2a - 3

What is the first step in substituting 'a + h' into f(x)?

• Subtract h from the function

• Add h to the function

• Replace x with a + h

• Multiply by h