12 Basic Functions Challenge Activity for Pre-Calculus

A few weeks ago, I had my best lesson of the year so far in pre-calculus as we were studying the 12 basic functions. My students were engaged like never before, and they became super competitive throughout the activity. They did way more questions than I ever would have been able to get them to do if I had just given them a homework assignment.

When they came into class the next day, they begged to do an activity similar to the previous day’s activity because it had been so much fun. Yes, students begging to do math. It made my heart smile.

When students entered the room, they found twelve lime green posters spread around the room. I created one poster for each of the 12 basic functions.

Each one of these posters represented one of the 12 basic functions identified in our Demana and Waits Pre-Calculus textbook.

Each of my 12 Basic Functions Posters contains the name of the function as identified by our book, a graph of the function, the equation of the function, and an interesting fact about the function.

My goal for this activity was to get students up and moving around the room and talking about the various parent functions. I originally thought about making these posters into small cards for each group to have at their desk, but the copy machine I had to use to do that ended up breaking which put a halt to that plan.

So, posters it was. And, I think that ended up being a good plan anyway.

The next resource I created for this activity was a challenge tracking sheet. Each group would have the opportunity to earn up to 16 stamps by completing 16 different challenges.

I find that a tracking sheet is necessary whenever I do activities like this, or groups do not end up managing their time wisely or they try to do the same problems over and over and over again. This way, students know exactly what has been finished and what still needs to be done.

After passing out a challenge tracking sheet to each group, I gave each group a ziplock bag containing 12 laminated cards that match the 12 basic functions posters surrounding the room.

MATH = LOVE RECOMMENDS…

A laminator is a MUST-HAVE for me as a math teacher! I spent my first six years as a teacher at a school with a broken laminator, so I had to find a way to laminate things myself.

I’ve had several laminators over the years. I currently use a Scotch laminator at home and a Swingline laminator at school.

• Scotch Laminator
• Swingline Laminator
• Nuova Laminating Pouches

I highly recommend splurging a bit on the actual laminator and buying the cheapest laminating pouches you can find!

When I was talking to my husband about my idea for this activity, he suggested that I make the cards double-sided and add a letter to the back to make the activity easier to check.

This turned out to be a LIFE-SAVER.

So, you are probably wondering by now what are the challenges?

The idea for this activity started when I was flipping through the textbook and a set of exercises caught my eye. The problems asked students to identify which of the 12 basic functions fit each description.

For example, identify “the four functions that are odd” or “the three functions with no zeros” or “the six functions that are increasing on their entire domains.”

I thought these were AMAZING questions, but I didn’t want to just hand them out as a textbook assignment. That sparked the idea for this challenge activity.

Not familiar with this textbook? You are in luck because Pearson has the PDF of this section of the textbook on their website for free!

The 12 Basic Functions are

• The identity function, f(x) = x
• The squaring function, f(x) = x^2
• The cubing function, f(x) = x^3
• The reciprocal function, f(x) = 1/x
• The square root function, f(x) = sqrt(x)
• The exponential function, f(x) = e^x
• The natural logarithm function, f(x) = ln x
• The sine function, f(x) = sin x
• The cosine function, f(x) = cos x
• The absolute value function, f(x) = |x|
• The greatest integer function, f(x) = int (x)
• The logistic function, f(x) = 1/(1+e^-x)

I especially loved that these questions killed two birds with one stone. They gave my students crucially needed practice with the new vocabulary words we had been learning (even odd, domain, range, continuous, point of discontinuity, bounded, increasing, decreasing, zeros, end behavior, etc.) and it introduced them to a whole bunch of parent functions at once.

Some of these were parent functions they were very familiar with from Algebra 1 and Algebra 2. Others (like the logistic, sine, cosine, and greatest integer functions) were completely new.

I typed up the challenges two to a page and printed them and laminated them. I only printed one set of challenges, but in retrospect I should have printed at least two sets so that two groups could be working on any one challenge at the same time.

There were a few challenges that students found especially tricky. This meant that other groups had to wait a really, really long time to be able to tackle that challenge since there was only one copy.

Given that I had set this up as a competition to see which group could complete the most challenges within our 50 minute period, this meant some students were very frustrated at the groups using the challenges that they still needed.

To kick off the challenge, I gave each group a challenge tracking sheet, bag of parent function cards, and one of the challenge cards (randomly chosen by me) to begin with.

Each group immediately set to work looking at the posters of the 12 basic functions around the room and debating which cards represented the correct answers. When they thought they had the answer, they would send a delegate from their team up to my desk with three things.

Their Challenge Tracking Sheet (for me to stamp if they were correct), their Challenge Card (so I could figure out where to look on my answer key), and the function cards that they believed answered the question.

I would flip over the cards that they brought me and quickly compare the letters to my answer key. If they were correct, I would stamp their sheet and let them change out their challenge card for a new challenge.

If they were incorrect, I would tell them simply that they were incorrect and send them back to rework the problem with their group.

I didn’t really get any pictures of my students in action during this activity because I was CONSTANTLY busy checking students work and handing out new challenges.

I overheard so many awesome conversations, and my students were VERY familiar with the basic graphs of the 12 basic functions by the end of the class period!

My students were super competitive which was good because it kept any groups from giving other groups the answers which can sometimes happen with activities like this.

I feel a bit weird being proud of this lesson because I don’t actually feel like I did much teaching about the 12 basic functions. My students did all the learning and teaching themselves. But, those really are the best lessons, aren’t they?