I know that they probably don’t need an “introduction” to functions. They’ve seen functions and they’ll be able to tell me all about the vertical line test (even if they don’t know why they use it). I see this lesson as a review of function notation, as well as a way for me to set the table for the relatively formal notation and understanding of functions they’ll use throughout the year. I will implement this lesson on the second day of class.

Their warm up will start here:

We’ll start the conversation about finding a “rule” that related the x-value to the y-value. I want them to start to look at these relations and see patterns (eventually they’ll recognize the types of patterns…e.g. linear, quadratic, etc.).

We’ll discuss the three big types of ways we’ll look at relations…coordinates, tables and graphs. I’ve found that my students don’t see them as three ways to represent the same thing. This will be the first time we have a chat about how an equation, a graph, a table, and coordinates all show the same thing; that the graph of an equation is not “the answer” they’re trying to get to match the back of the book.

We’ll then discuss the domain and range of a relation. They’ll be used to the idea, but I expect them to struggle with any representation that isn’t a set of coordinates:

Then comes the time to discuss a function. I found a video a few years ago that some group of teachers made and posted to youtube. It is by far the most entertaining input/output video I’ve ever seen:

I didn’t make that video, but I thoroughly enjoy watching my students experience it in class!

Next, we’ll define a function and work with that definition:

We’ll refer back to the idea of domain and range so that my students can decide that a vertical line test will work on a graph to determine functionality. I’m going to post the slide that I currently have for this, but looking at it now, I’m going to change it.

Then we’ll discuss function notation:

And finally, we’ll bring it all together with them creating their own function:

This last slide is the most important. I will emphasize with them that a function relates two variables. The input gives you one value for an output. The number of hours gives you an amount in the bank account. My goodness, that’s such an important idea. An input gives you an output. We’ll be using that all year!