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INPUT/OUTPUT

The input and output of a function- is the independent (input) and dependent (output) variables. You can think of inputs as the X-axis values and outputs as the Y-axis values. They can be related to time, temperature and many other related scenarios. Normally, it is easier to think of inputs and outputs using an example.

Let’s consider heating water until it starts to boil….

We start boiling our pot of water at 0 minutes (when we initially place the pot over the stove) and the temperature of the water is 25 degrees Celsius, which is considered room temperature.

In this case the input is the 0 minutes and the output is the 25 degrees.

Lets assume that the temperature increases by two degree every minute. Our formula is as follows:

T= 2t+25

INPUTS (t)                                                    OUTPUTS (T)

0 minutes                                                     25 degrees

5 minutes                                                     35 degrees

10 minutes                                                  45 degrees

15 minutes                                                  55 degrees

20 minutes                                                  65 degrees

           

Based on out formula, we can clearly see the inputs and outputs of this scenario. Inputs and outputs can be applied to many different situations. This heating water scenario is just one example.

It is very important to note that inputs and outputs of a function need to have a relationship. So you cannot simply pair random numbers and call them input and output. In our case, time and water temperature are related. We found our outputs through our formula.

Finally, this specific example is a mathematical model because the output(temperature) DEPENDS on the output (time). Without the time, we cannot determine the temperature. This makes the input the independent variable and the output the dependent variable.