Function Composition and Evaluation

Mr. Bean introduces the concept of function composition in AP PreCalculus, explaining how to compose functions using values, tables, and graphs. He covers alternative notations and the identity function, providing examples and practice problems to reinforce understanding. The lesson is divided into sections, each focusing on different aspects of function composition, ensuring a comprehensive understanding of the topic.

What is the main idea behind composing functions?

• Adding two functions together

• Subtracting one function from another

• Multiplying two functions

• Substituting one function into another

In the expression f(g(x)), what does g(x) represent?

• The difference between f and g

• The sum of f and g

• The input for f

• The output of f

How is the composition g(f(x)) different from f(g(x))?

• It uses different functions

• It starts with the function g

• It results in the same output

• It is not a valid composition

What does the circle symbol (∘) in f ∘ g(x) indicate?

• Addition of functions

• Subtraction of functions

• Composition of functions

• Division of functions

When using a table of values, what is the first step in finding f(g(x))?

• Find the input for g

• Find the output of f

• Find the output of g

• Find the input for f

In a table, if g(0) = 3, what is the next step to find f(g(0))?

• Find g(0)

• Find f(0)

• Find g(3)

• Find f(3)

How do you identify the output of a function from a graph?

• By looking at the x-axis

• By looking at the y-axis

• By finding the slope

• By finding the intercept

What is the output of f when the input is -1, given f is a parabola?

• 2

• 3

• 1

• 0

What is the additive identity?

• Infinity

• -1

• 1

• 0

If f(x) = x, what is f(g(x)) equal to?

• f(g(x))

• x

• g(x)

• f(x)