Composition of Functions

You have tons of paper scattered all over the table. While trying to solve a problem, you notice you have to flip back and forth between two equations that are related to each other to get a final answer. Isn't there a way to combine these two functions to reduce the work and solve for the final answer quicker? Luckily for us there is a process that can do exactly what we're looking for in resolving this issue. In this lesson we're going to be focusing on composition of functions and the process of creating them.

Grade Level: 11th grade Pre-Calculus

Time Frame: 2 – 3 days

Purpose: I want all student to understand the vocabulary: functions, function notation, and composition of functions. In addition, they should be able to create and apply composition of functions.

Objectives: The students should also be able to represent a given function as a composite function of two or more functions. They will later be able to answer questions in independent work and create their own composition of functions.

Your mission:

Your goal is to complete the warmup, watch video, create and solve your own composition of functions, the exit ticket as well as work on the website for extra practice. Afterwards, you will demonstrate your comprehension on the concept with an quiz.

            As I was saying earlier, we are going to be focusing on composition of functions. This is a brand-new topic, but do not get discouraged. Through some hard work and practice, you will be able to understand some important vocabulary and be able to utilize the process of composition of functions in real life. Composition of functions is all about how one input and output of function relates to another function’s input as well as output. By finding the relation between the two functions, we can cut down on extra work and discover how the functions affect each other. Let's get started!

1. Warmup - In this task, you will answer the questions on the google doc. Make sure to follow the directions in the document.   https://docs.google.com/document/d/1cVHQ5y_DERDZnh_A4NaZ7so3gLtYYncMoeeM3ADldDg/edit?usp=sharing
2. Watch video and Create - Make sure to watch the video completely, since it will help you learn the the process of the concept. Afterwards, open the google doc and create 2 functions of your own. With these 2 functions, create 2 composition of functions and post them to the google doc. The doc will have more instructions.   https://docs.google.com/document/d/1v1Kx0pw1g8NHfNHAjcQTv3WCaAsoForQKXc7kn30pis/edit?usp=sharing                                                      https://pro.panopto.com/Panopto/Pages/Viewer.aspx?tid=fd7e136e-0a15-44fc-b21e-ace2006bceb5
3. Exit ticket - In google doc, answer the questions and post your answers to it.  https://docs.google.com/document/d/1wRvqLmfGj-8al5rTThQUFDi8gMXHU-V2DU1VFD9_1cI/edit?usp=sharing 
4. Extra practice - This website provides extra practice on answering composition of functions questions. https://www.mathsisfun.com/sets/functions-composition.html
5. Test your knowledge - After completing the previous steps, complete the following quiz. Do not post your answer to this document. Create a separate document and e-mail it to me.   https://docs.google.com/document/d/16Fw5aPYgShCgm8yqDfxrRaq_rz6ypQPi689htChBAs4/edit?usp=sharing
6. Closure - Answer the closure questions on the document.  https://docs.google.com/document/d/107SmVgfYVEC3pCVgZc0V4MMkySUBeuaz5hho3UlsSW4/edit?usp=sharing

*This is the rubric to follow and make sure that you do the assignments correctly. *

https://docs.google.com/document/d/1p6OvkGjzyljd2EAnFRLLK9UXROdtpnvBHhfvZx_Jeqg/edit?usp=sharing

Reminder- This will be our first time using google docs as a means to finish our work. Do not panic! If you have questions feel free to e-mail me. Do not edit the questions or instructions on the google docs. In addition, post only once on each doc and include your name by each answer to receive credit. I will check each answer do not just copy each other's answers. 

I will do a quiz for the students at the end of the lesson to check student understanding. The rubric will be based on completion, quality, as well as regular grades for warmup, creation, exit ticket, and quiz. The website is extra practice and will be not taken for a grade. However, I still suggest the students take the time to engage in the website. The rubric I will use to grade the students is provided at the bottom which has more details on the grading. The grade scale is out of 100.

https://docs.google.com/document/d/1p6OvkGjzyljd2EAnFRLLK9UXROdtpnvBHhfvZx_Jeqg/edit?usp=sharing

Congratulations, you have completed the lesson on Composition of Functions. You have done a lot of work and explored the concept on a new format - WebQuest. Now, when looking at functions, you will be able to look for connections as well as how inputs and outputs relate to each other. 

Reflection Topics (Please post your responses on the google document.):

How does the lesson relate to me in real life?

Where would I see these types of problems?

Do you think you will ever use this knowledge later?

https://docs.google.com/document/d/107SmVgfYVEC3pCVgZc0V4MMkySUBeuaz5hho3UlsSW4/edit?usp=sharing

                                                                                    Works Cited

      Chapter 111. Subchapter C. (n.d.). http://ritter.tea.state.tx.us/rules/tac/chapter111/ch111c.html. 

      Composition of Functions. (n.d.). https://www.mathsisfun.com/sets/functions-composition.html.

       Leos, C. (2021, May 10). Pre- Calculus: Create.

       Leos, C. (2021, May 10). Pre-Calculus WebQuest Rubric.

       Leos, C. (2021, May 10). Pre-Calculus: Closure.

       Leos, C. (2021, May 10). Pre-Calculus: Exit Ticket.

       Leos, C. (2021, May 10). Pre-Calculus: Quiz .

       Leos, C. (2021, May 10). Pre-Calculus: Warmup.

The lesson for this webquest was intended for 11th grade students under the Texas Essential Knowledge and Skills and meets the following TEKS standards:

Mathematics TEKS:

§111.42. Precalculus, Adopted 2012 (One-Half to One Credit). 

(2)  Functions. The student uses process standards in mathematics to explore, describe, and analyze the attributes of functions. The student makes connections between multiple representations of functions and algebraically constructs new functions. The student analyzes and uses functions to model real-world problems. The student is expected to:

(C)  represent a given function as a composite function of two or more functions