Your First Function
Great job! I've copied your model below. It's the red curve. This model is your first example of a function.
This particular function has a very specific job: if you give it a time as an "input", then this function makes an estimate of the height of the missile at that time and returns it as an "output". Geogebra made this function using something called "statistical regression". We won't study regression in this book, but there's nothing to stop us from using it.
You can click and drag the blue point to see all the predictions of the model. The x coordinate of the point represents a time "input", and y coordinate represents the "output" which is the estimated height at that time.
Play around! Move the blue point; scroll around and see what you can learn from the model; you can click and drag to pan, or scroll with your mouse to zoom in and out. Don't worry about breaking anything. If you ever get lost in any activity, just click the circular arrows in the top right of an app to reset it.
Quick Check: At time 45 seconds, what does the model predict the height of the missile will be?
Here's a few more open ended questions to think about as you explore: How high does the model predict the the missile will get? What time does the model predict this will occur? When does the model predict the missile willl land? Why does the model predict that the missile will go below the horizontal axis? Don't worry too much about answering all of these questions. But take a moment and think about them on your own.
In the next lesson we'll investigate more closely how high the missile will get. Later in this course we'll discuss the others as well.
After you're done exploring, scroll down and move forward to the next activity.