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

Tags

CCSS.HSF-BF.A.1C

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

Tags

CCSS.HSF-BF.A.1C

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

Tags

CCSS.HSF-BF.A.1C

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

• Addition of functions

• Subtraction of functions

• Composition of functions

• Division of functions

Tags

CCSS.HSF-BF.A.1C

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

Tags

CCSS.HSF-BF.A.1C

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

Tags

CCSS.HSF.IF.A.2

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

• 2

• 3

• 1

• 0

Tags

CCSS.7.NS.A.1B

What is the additive identity?

• Infinity

• -1

• 1

• 0

Tags

CCSS.HSF-BF.A.1C

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

• f(g(x))

• x

• g(x)

• f(x)

Tags

CCSS.HSF-BF.A.1C