Operations of Functions

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Objective

SWBAT evaluate and graph new functions found by using function operations

Big Idea

Addition, subtraction, multiplication and division of functions will be reviewed by students developing group presentations on the operations. Function notation will be analyzed to reduce misconceptions.

Bell Work

5 minutes

The bell work asks students to subtract and multiply polynomials.  This is a quick review so students work for about 4 minutes before the processes are put on the board

The work reminds students subtracting the entire second polynomial instead of just the first term which is the most common error. Some students need reminded about how to multiply two polynomials but seeing the others students work, makes students oh yeah I forgot.

Presentation Development

10 minutes

I now tell students that today they will be writing a lesson to review operations of functions along with introducing the notation used in the Larson, "Precalculus with Limits, 2nd edition" text.

My students have done addition, subtraction, multiplication and division of functions in prior courses.  This activity gives students a quick review and has the students consider the common errors made when doing function operations. Students also compare the domains of the original functions with the domain of the resulting function.

I  briefly explain the activity to the class. I let students know that their groups project will be the instruction over a function operation. I will not do any instruction on the operation. The groups will  develop between 3 and 5 questions on the presented operation  for students to do as homework. The groups can present using a document camera, a Powerpoint any other presentation tool. The presentation needs to be clear and students should be prepared to answer other students questions.

Organizing the activity:

Students put themselves into group of 3 to 4 students. I pick the groups size so that I have 4 different groups. One person from each group comes to me my desk.  I ask each person to give me a number from 1-50 whoever is closet to the number I have on a card pick a card from a stack of 8 (2 for each operation). Once that person has picked a card I remove the card that matches that operation and reshuffle the stack The next person who was closest to the my number picks etc. This continues until all the groups have an operation to do.

Students receive focus questions to help them determine some of the key concepts they need in for the presentations. 

 

Working on Presentations

25 minutes

The rest of  class is spent by groups developing their presentations. Students may use their book or several other books I have as references to help them understand.  I also allow students to use their phones, tablets or laptops if they want to do Internet research.

While students are working I move around to answer questions, review the presentations and ask questions of the groups. If a presentation is not clear I ask questions that may be asked by the class. I may say;"What did you do in this step? or How can you do that?"

One of the main concepts I work with is how to determine the domain of the result.  I give students two functions such as f(x)=x+3 and g(x)=sqrt(x). The students are asked to find the domain for f and g.  I then have the students complete the operation and ask "What is the domain for your answer?"  For addition, subtraction and multiplication students begin to see that the most restricted domain of f and g is the domain of the answer.  Division is different.  With that group I discuss when a fraction is undefined.  The students quickly see how to determine the domain of a division problem.

I pick g(x)=sqrt(x) because the domain is not all real numbers. The students usually pick polynomials when demonstrating how to work with the function operation. I could also use a rational expression if the students need more direction

Closure

5 minutes

With about 5 minutes left in class I have the groups clean up.  I remind the groups that we will be presenting during the next class. Some of the groups  assign work for group members to do so they will ready for the presentations.