## Jason M. Grant

Assistant Professor of Computer Science

## Functions

### Functions without Input or Output

Functions are often thought of as “boxes” that take some data as input and return some sort of output. A function is not required to have either an input or an output. Let’s start with a few basic examples.

In mathematics, the equation for a line can be written in the form of y = ax+b. We can also refer to y as a function of x. Therefore, we can rewrite the same equation as f(x)=ax+b, where  is our function and  is the input. Let’s assign the value of 2 to a and 5 to b. Now, f(x)=2*a+b . This produces the following graph.

A function in Python can be defined very similarly. If we name our function f, then the function can be declared as such:

def f(x):    return 2 * x + 5

Notice the format of the function in Python. Each function begins with def, followed by the name of the function, its arguments (input), and a colon. Lastly, the function returns the output with using the keyword return followed by the value it is returning.

Below is an example of a function that does not have a input nor does it return an output, but inside the function it makes several print statements to the user, another method of output which we have see before.

### Calculating the Area of a Circle

Let’s look at another example of a function, which calculates the area of a circle. Based upon our knowledge from geometry, we use the formula

to calculate the area. Thus, for any radius , we can calculate the area since  is a constant. One way for us to write this function would be to define  for a given number of significant digits.

pi = 3.141592654

Another way would be to import a module that already defines the value of pi. Notice line 1 of the program that imports the math module. Next, in line 6, the value of pi is obtained by calling math.pi.

### Calculating the Volume of a Circle

In this section, we compute the volume of a cone using two approaches. One approach would be to calculate the volume using the same methodology from the area of a circle function. The formula for the volume of a cone can be expressed as

. Now, we have two input variables. To create a function in Python with two input variables, we define the function as such:

def functionName( var1, var2):

The function for the volume of a cone can be found on line 8. Another way to define the volume of a cone would be to do so in terms of the area of the base circle. Since, we already have a formula for the area of a circle, we could use this function in our new function definition for the volume of a cone. Notice that both lines 18 and 19 print the same value.

### Calculating Overtime

This example calculates base pay plus additional pay for overtime work, based upon a 40 hour work week. In this function, we introduce the if/else statement as well. We will explore conditional statements in more detail in one week. 