Unlocking Periodic Functions: Identifying Patterns and Predicting Values

Algebra 2 Grades High School 5:34 Video
Print Lesson Plan Watch Video

Lesson Description

This lesson explores periodic functions, focusing on how to identify them from graphs, determine their period, and calculate function values for given inputs, including large and negative values.

Video Resource

Is a Function Periodic?

Mario's Math Tutoring

Duration: 5:34
Watch on YouTube

Key Concepts

  • Periodic Function
  • Period of a Function
  • Function Evaluation

Learning Objectives

  • Students will be able to identify periodic functions from their graphs.
  • Students will be able to determine the period of a periodic function.
  • Students will be able to calculate function values for periodic functions, even for large or negative input values, by utilizing the concept of periodicity.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of a function and its graphical representation. Briefly discuss the concept of repeating patterns in everyday life (e.g., seasons, heartbeats) as an analogy to periodic functions.
  • Video Presentation (10 mins)
    Play the video 'Is a Function Periodic?' by Mario's Math Tutoring. Encourage students to take notes on the key definitions and examples provided in the video.
  • Guided Practice (15 mins)
    Work through examples similar to those in the video, emphasizing the process of identifying periodic functions, finding the period, and calculating function values. Provide scaffolding as needed.
  • Independent Practice (15 mins)
    Assign practice problems where students apply the concepts learned. Encourage students to work in pairs or small groups to discuss their solutions.
  • Wrap-up and Assessment (5 mins)
    Review the key concepts and address any remaining questions. Administer the multiple-choice and fill-in-the-blank quizzes to assess student understanding.

Interactive Exercises

  • Graph Matching
    Present students with a set of graphs and ask them to identify which ones represent periodic functions and to determine their periods.
  • Value Prediction
    Provide a periodic function (graphically or algebraically) and ask students to predict the function value for a given input, requiring them to use the concept of periodicity.

Discussion Questions

  • What are some real-world examples of periodic phenomena?
  • How can you visually determine if a function is periodic?
  • How does knowing the period of a function help you calculate function values for large or negative inputs?

Skills Developed

  • Critical Thinking
  • Problem Solving
  • Pattern Recognition

Multiple Choice Questions

Question 1:

Which of the following best describes a periodic function?

Correct Answer: A function that repeats its values at regular intervals.

Question 2:

The period of a periodic function is:

Correct Answer: The length of one complete cycle of the function.

Question 3:

If a function f(x) has a period of 3, then f(x) = ?

Correct Answer: f(x+3) = f(x)

Question 4:

Which of the following graphs represents a periodic function?

Correct Answer: A sine wave.

Question 5:

If a periodic function has a period of 5 and f(2) = 3, what is f(7)?

Correct Answer: 3

Question 6:

A function is periodic if its graph:

Correct Answer: Repeats itself after a certain interval.

Question 7:

What is the period of the function shown in the graph (imagine a sine wave with a period of 4)?

Correct Answer: 4

Question 8:

A non-periodic function:

Correct Answer: Does not have a repeating pattern.

Question 9:

If f(x) is a periodic function with period P, then f(x + 2P) is equal to:

Correct Answer: f(x)

Question 10:

Which of the following is NOT a periodic function?

Correct Answer: x^2

Fill in the Blank Questions

Question 1:

A function is considered ___________ if its values repeat at regular intervals.

Correct Answer: periodic

Question 2:

The __________ of a periodic function is the length of one complete cycle.

Correct Answer: period

Question 3:

If f(x) has a period of 7, then f(x) = f(x + _______).

Correct Answer: 7

Question 4:

A function that does not have a repeating pattern is called __________.

Correct Answer: non-periodic

Question 5:

Knowing the __________ of a function allows you to calculate function values for inputs outside the displayed graph.

Correct Answer: period

Question 6:

The sine and cosine functions are examples of ___________ functions.

Correct Answer: periodic

Question 7:

If f(x) is periodic with period P, then f(x - P) = f(__________).

Correct Answer: x

Question 8:

To determine the period visually, find the shortest horizontal distance before the graph __________.

Correct Answer: repeats

Question 9:

If a function's period is 6, then f(12) will have the same value as f(_______).

Correct Answer: 6

Question 10:

For a periodic function, the y-values __________ after each period.

Correct Answer: repeat

Educational Standards

A2.F.1:Understand functions as descriptions of covariation (how related quantities vary together). A2.F.1.1: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

Download ready-to-use materials for this lesson:

Student Worksheet Classroom Slides Assessment Quiz
Add to Google Classroom

User Actions

Sign in to save this lesson plan to your favorites.

Sign In

Share This Lesson

Related Lesson Plans