What Is a Function?

Functions Are Prebuilt Tools

A function is a small, reusable piece of code that someone else has already written for you, packaged up under a short name so that you can use it without needing to know (or care) exactly how it works internally.

Think of a function like a kitchen appliance. A blender doesn’t require you to understand its motor or wiring. You put ingredients in, press a button, and get a smoothie out. R functions work the same way:

  1. Input — you give the function some data to work with.
  2. Operation — the function does something to that data (behind the scenes).
  3. Output — the function gives you back a result.

Input → Function (does the operation) → Output

How Functions Are Named

You will almost always be able to quickly identify the functions in a piece of R code by the fixed pattern: FUNCTION_NAME(). That is, an R function is called by writing the function’s name followed immediately by an opening parenthesis. The following list shows some commonly encountered R functions.

  • mean()
  • sum()
  • c()
  • round()
  • sqrt()

So, any time you see a word immediately followed by parentheses in R code, you’ve found a function call.

Practice: Spot the Functions

Which of the following lines contain a function call? Predict your answer, then check it against the solution.

x <- 7
y <- sqrt(49)
z <- x + 2
w <- round(3.14159, 2)
  • x <- 7 — No function call. Just assignment of a literal number.
  • y <- sqrt(49) — Yes, sqrt() is a function call.
  • z <- x + 2 — No function call. Just arithmetic on an object.
  • w <- round(3.14159, 2) — Yes, round() is a function call.

Why This Matters

Almost every useful thing you’ll do in R, from simple calculations to complex statistical models, involves calling functions. Getting comfortable spotting them, and understanding the input → operation → output pattern, is the single most important conceptual step in this tutorial. Everything else builds on it.

Going Further: Functions as Mathematical Formulas

If you’re comfortable with algebra, it can help to know that R functions work in essentially the same way as mathematical functions. Feel free to skip this box entirely if it doesn’t help you.

The following equation represents a linear function of \(x\).

\[ f(x) = 1.5 + 2x \]

For any value of \(x\) that we provide as input, \(f(x)\) first multiplies that value by 2 and then adds 1.5 to the resulting product. So, if we let \(x = 3\), we get \(f(3) = 7.5\).

\[ \begin{align*} f(3) &= 1.5 + 2 \times 3\\ &= 7.5 \end{align*} \]

The mean() function we used to motivate these ideas operates through the same conceptual process. If we let \(n\) represent the number of values in \(x\), we could notate the mathematical definition of the mean() function as follows.

\[ \begin{align} f(x) = \frac{1}{n}\sum_{i = 1}^{n} x_i \end{align} \tag{1}\]

Doing the analogous calculation in R would look like the following.

a <- 1:5
mean(a)
[1] 3

In most of your R analyses, you won’t need to worry about defining the functions you use: that work has already been done by the developers who wrote the packages you’re using. You will usually only have to worry about preparing the input, calling an appropriate function, and processing the function’s output.

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