Decoding Composition: Mastering Functions with Tables

Algebra 2 Grades High School 4:19 Video
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Lesson Description

Learn how to evaluate composite functions using tables! This lesson provides a step-by-step guide to understanding notation and applying double substitution to solve problems.

Video Resource

How to do Composition of Functions Given a Table

Mario's Math Tutoring

Duration: 4:19
Watch on YouTube

Key Concepts

  • Function Notation
  • Composition of Functions
  • Double Substitution
  • Evaluating Functions from Tables

Learning Objectives

  • Students will be able to evaluate composite functions given a table of values.
  • Students will be able to correctly interpret and apply the notation for composition of functions.
  • Students will be able to identify the correct order of operations when evaluating composite functions.

Educator Instructions

  • Introduction (5 mins)
    Briefly review function notation and the concept of evaluating a function at a given value. Introduce the idea of a 'function machine' where an input goes in, and an output comes out.
  • Video Presentation (10 mins)
    Play the YouTube video 'How to do Composition of Functions Given a Table' by Mario's Math Tutoring. Encourage students to take notes on the notation and the double substitution method.
  • Guided Practice (15 mins)
    Work through the examples in the video again, pausing to explain each step in more detail. Emphasize the importance of working from the inside out.
  • Independent Practice (15 mins)
    Provide students with additional practice problems involving composition of functions using tables. Circulate to provide assistance as needed.
  • Wrap-up & Assessment (5 mins)
    Summarize the key concepts and answer any remaining questions. Administer the multiple-choice and fill-in-the-blank quizzes to assess understanding.

Interactive Exercises

  • Think-Pair-Share
    Present a composition of functions problem using a table. Have students individually work on the problem, then pair up to discuss their solutions and reasoning. Finally, share solutions with the class.
  • Error Analysis
    Present a worked-out solution to a composition of functions problem with a deliberate error. Have students identify the error and explain how to correct it.

Discussion Questions

  • Why is the order of operations important when evaluating composite functions?
  • How does using a table to evaluate functions differ from using an equation?
  • Can you think of real-world examples where composition of functions might be used?

Skills Developed

  • Critical Thinking
  • Problem Solving
  • Attention to Detail
  • Understanding Function Notation

Multiple Choice Questions

Question 1:

Given f(2) = 3 and g(3) = 5, what is g(f(2))?

Correct Answer: 5

Question 2:

Which notation correctly represents 'f of g of x'?

Correct Answer: f(g(x))

Question 3:

When evaluating f(g(x)), which function do you evaluate first?

Correct Answer: g(x)

Question 4:

If f(x) = x + 1 and g(x) = 2x, what is f(g(1))?

Correct Answer: 3

Question 5:

In composition of functions, the output of the inner function becomes the ______ of the outer function.

Correct Answer: input

Question 6:

Using the table, if f(-1) = 2 and g(2) = 4, then g(f(-1)) equals:

Correct Answer: 4

Question 7:

What is the first step in evaluating a composite function using a table?

Correct Answer: Find the output of the inner function.

Question 8:

Given f(0) = 1 and g(1) = -2, find f(g(1)).

Correct Answer: -2

Question 9:

If g(x) = x^2 and f(x) = x - 3, what is g(f(4))?

Correct Answer: 1

Question 10:

What does f(g(x)) mean?

Correct Answer: f of the quantity g of x

Fill in the Blank Questions

Question 1:

The process of using the output of one function as the input of another is called _________ of functions.

Correct Answer: composition

Question 2:

When evaluating g(f(x)), you start by evaluating the function that is the _______ function.

Correct Answer: inner

Question 3:

If f(x) = x + 5 and g(x) = 2, then f(g(x)) = _______.

Correct Answer: 7

Question 4:

The input of the composite function is the x-value and the output is the ____-value.

Correct Answer: y

Question 5:

Given a table, to find f(g(a)), first locate g(a) then use that value to locate _______.

Correct Answer: f(g(a))

Question 6:

Evaluating a composition of functions is similar to a _______ substitution.

Correct Answer: double

Question 7:

If f(3) = 7 and g(7) = 10, then g(f(3)) equals _______.

Correct Answer: 10

Question 8:

In the notation f(g(x)), g(x) is the _______ function.

Correct Answer: inner

Question 9:

When using a table, the _______ values are located in the table and used as inputs.

Correct Answer: x

Question 10:

If f(x) = 2x and g(x) = x-1, then f(g(2)) = _______.

Correct Answer: 2

Educational Standards

A2.F.1:[Standard] Understand functions as descriptions of covariation (how related quantities vary together). A2.F.1.1:[Objective] Use algebraic, interval, and set notations to specify the domain and range of various types of functions, and evaluate a function at a given point in its domain.

Teaching Materials

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