Professor Aissi: Lesson On Functions (Nathalie Aissi)

Hello class, my name is Professor Aissi and today, we are going to learn about Functions! Yay!

So what is a function class?

  A function is a rule that takes particular numbers as inputs and for each input number, there is an output number. Basically, one output for every input is a function.  

Below is an example of having an output value for every input value. In this case, you can see that for the different temperatures (output), there is a time (input) for each temperature value. This is what a function is ladies and gentlemen!

                              

Time (input)	Temperature (output)
0 (hour)	85 (degrees Fahrenheit)
1 (hour)	86 (degrees Fahrenheit)
2 (hours)	88 (degrees Fahrenheit)
3 (hours)	89 (degrees Fahrenheit)
4 (hours)	88 (degrees Fahrenheit)
5 (hours)	87 (degrees Fahrenheit)

One thing about a function is that it can be represented in many different ways! For example, a function can be represented in a table form (like the example above), in a graph form, in a formula or even in words.

Example of a function represented in a formula:  Y=3x + 12 . To write this formula, you use the slope intercept form, y=mx+b, where “m” is the slope of the function, “b” is the initial value, “x” is the input value and “y” is the output value.

Example of a function represented in Function Notation:  Output= f(input)

Ex: T=f(h),  which is temperature= f(time).

Example of a function represented in words: In one hour, the temperature was 86 degrees Fahrenheit. In two hours, the temperature was 88 degrees Fahrenheit. In three hours, the temperature was 89 degrees Fahrenheit.

Example of a function represented in a graph is below:

 (Every input value graphed has an output value because without every input having an output, a function would not exist. )

                                

Now class, another important thing about a function is that it has to pass the vertical time test!

The vertical line test is the idea of single valued means that no vertical line ever crosses more than one value. If a graph does not pass the vertical line test, then the graph is not a function!! For example, the graph above passes the vertical line test because if a vertical line is placed on any part of the graph, the line would not cross more than one value.

Below is an example of a graph that is not a function because it doesn’t pass the vertical line test:

                                       

You can see on that for the graph above, if a vertical line was placed on the graph, the vertical line would cross more than one value and a function can only cross one value.

When you use a function to describe an actual situation, the function is called a mathematical model. A mathematical model is a function in which the output values depend on the input values.

An example of a mathematical model: T=1/4R+40 is a mathematical model of the relationship between the temperature and the cricket’s chirp rate, This means that when the cricket’s chirp rate is, lets say6, 60 chirps per minute, the temperature is 70 degrees Fahrenheit, which means that the chirp rate depends on the temperature.

An example of a non- mathematical model:

           

                                     Passing Yards for Tom Brady

Year	Passing Yards
2010	3000
2011	5114
2012	2681
2013	6381

The graph above represents how many passing yards Tom Brady threw each year. But even though this is a function, this is not a mathematical model function because the output (passing yards) do not depend on the input (years). In other words, the number of passing yards done by Tom Brady is not dependent on the year he did it.

Now class, here is all there is about functions! Congratulations, you guys are experts now!