1. Alex and Function

2. Once upon a time, much like today, Alex was sitting in math class. The weather in Chicago was frightful. Today there had already been snow, sleet hail, rain, and subzero temperatures. Alex was a good student, and always took his notes, but today it seemed like his teacher was just writing gibberish on the board. Alex wanted to listen to his teacher talk about functions, but his strategy of holding his eyes open wasn’t working.

3. Alex didn’t want to be in class today, he wanted to be traveling the world. He began to think about pizza, France, warm weather, and a beach down in Mexico. Alex started to doze off to sleep.

4. Alex looked around and saw palm trees and sandy beaches. Wow! He thought, this is way better than being in math class! He started to walk down the beach, when all of a sudden he came across a jelly fish that seemed to be crying. A jelly fish crying he thought, what weird dream world am I in?

5. Alex approached the jelly fish and asked, “What is your name?” The jelly fish stopped crying just long enough to mumble, “My name is Function”. What a weird name thought Alex, who would name their jelly fish Function? Alex then asked the jelly fish, “Why are you crying, Function?” Function looked up at Alex and said, “There is no reason to tell you, because you cannot help me”. The tears continued to fall, and Alex just felt awful, he wanted the jelly fish to stop crying so he agreed to help the jelly fish.

6. Function the jelly fish looked up, and said “Are you joking or can you really help me? This is not an easy task, it might take us a very long time!” Alex had nothing else to do, so he agreed. Function began to explain that his teacher assigned a project where all the students in the class had to figure out the true meaning of their names, and had to put together a presentation that they would present to the class. Function was not only worried about having stage fright in front of his class, but he also had no idea what function meant.

7. Alex knew a little bit about functions, because they were talking about them in math class, and he too had struggled with stage fright, so he knew that he would be able to help out the jelly fish. I CAN HELP YOU!

8. Alex told Function that they were going to start out learning about what a function represented. In the sand Alex wrote the definition of a Function. Function: a relation between a set of inputs and outputs, where each input has a unique output.

9. “What does that mean?” asked Function? Alex then went on to explain, if we think about the domain, which is all of the possible inputs, and the range, which is all of the possible outputs. Each input must match with exactly one output. Alex then drew in the sand an example of a mapping diagram.

10. The jelly looked a little confused, so Alex asked what he was thinking. Jelly thought for a second, and then asked, “What if there are multiple x-values that match with a single y-value, would that be a function?” Alex replied, “Yes as long as each input matches with a single output value”.

11. The jelly understood, but he wondered what a function looked like, so Alex drew multiple graphs in the sand. Function was very confused, how could all of these be a Function? They all look soo very different!

12. “Remember the definition of a function? All inputs must have a single output value!” “Oh, said Function, so I need to make sure that each x-value matches with a single y-value?” “Yes” replied Alex. Alex chuckled, “they are not all functions, and you need to determine whether or not they are a function!” “How can I possibly do that?” asked Function.

13. Looking at the graphs in the sand, Jelly tried to tell which graph was a function, but he was again stuck. Alex said to him, my teacher taught me to use the vertical line test. If you draw vertical lines on your graph and it touches the graph more than once, then it is not a function, because that will mean that the input has more than one given output.”

14. Function started drawing vertical lines on the graphs, and identified the functions drawn in the sand. Alex scanned his answers and shouted, “You are correct Function!”

15. “Alex, I have learned so much about functions today, and I now know what my name means, but can you help me determine what a function is used for?” said Function. Alex really wanted to answer this question, but he did not know the answer either! His teacher was talking about that, but he dozed off to sleep. “I am not sure jelly, but maybe someone on this island will be able to help us! Let’s walk down the beach and see if someone can help us.”

16. They started to walk down the beach when they came across two crabs arguing with each other. One of the crabs yelled at Function and Alex, “Hey you two, come over here we need help!” They walked over to the crabs and saw two drawings in the sand.

18. “A function models the relationship between the input and the output of a given situation. In this case, the input, or the domain, is the time, and the output, the range, is the distance traveled.” Alex started to remember his teacher talking about this and he knew that he could explain the graphs, and determine who finished the race quicker.

22. “Well…” said Alex we have to take a closer look at the numbers that are on these graphs, and at a table of values. Looking at the graphs the table of values would look like this. Alex drew two tables in the sand, and explained the numbers in the table represented the domain and range.

24. Function and Alex started to walk down the beach again. “Thank you Alex, I now know what my name means, represents, and how I could use it in real life. I just need to work on my fear of public speaking!” “Your welcome Function, but I think that you know so much about your name now that you will do just great!” Said Alex. You will do great!!

25. RING!!! RING!!!! RING!!! Alex starts to open his eyes and sees the class leaving the room. Alex packs up his things, and thinks to himself, thank goodness that I have such a good math teacher, because if I didn’t I would have never been able to help Function discover the true meaning of his name.