# Plot of a function in ggplot incorrectly showing as a constant line

## Issue

I want to plot polynomial functions of high degrees with given coefficients. I created the function `f_erzeuger()` in order to write a polynomial function `f` to be able to plot it with ggplot2 and `stat_function(fun = f)`. `coef` is a vector of coefficients for the polynomial function.

``````f_erzeuger <- function(coef) {
f <- function(x) {
x_vec <- c(1, x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10)
d <- length(coef) - 1 # degree of the polynomial
sum(coef * x_vec[1:(d+1)])
}
f
}
``````

However ggplot2 is not able to plot this curve, probably because the function doesn’t actually calculate a function term.

``````f <- f_erzeuger(c(4, 5, 2))
ggplot(data.frame(x = c(-50, 50)), aes(x = x)) +
stat_function(fun = f, color = "blue") +
stat_function(fun = function(x){3 + 5*x + 2*x^2}, color = "red")
``````

`f` is showing as a constant line even though it should be a polynomial.

## Solution

The problem is that your function is not vectorized. Running `?stat_function` and looking at the documentation for `fun`:

`fun`: Function to use. Either 1) an anonymous function in the base or rlang formula syntax (see `rlang::as_function()`) or 2) a quoted or character name referencing a function; see examples. Must be vectorised.

To make the function vectorized, we need to make sure that, for example, `f(c(0, 1))` will return `c(f(0), f(1))`. Note that one issue in your function is the line where you define `x_vec = c(1, x, ...)`. This wouldn’t work if `x` were a vector with more than one element.

There are many ways to vectorize your function. I will do it using the tidyverse (mainly `purrr::map()`).

``````f_erzeuger = function(coef) {
function(xvals) {
d = length(coef)
map_dbl(xvals, function(x) {
x_vec = x ^ (0:(d - 1))
sum(coef * x_vec)
})
}
}
``````

The changes made to this function:

• Most importantly, the function is now vectorized.
• Instead of defining `x_vec` explicitly to degree 10, we can leverage the fact that `^` in R is vectorized (so `x^(0:2)` is the same as `c(1, x, x^2)`).
• We can return the function directly inside `f_erzeuger()` instead of defining `f` and then returning it.

Now things will work as expected:

``````f <- f_erzeuger(c(4, 5, 2))
ggplot(data.frame(x = c(-50, 50)), aes(x = x)) +
stat_function(fun = f, color = "blue") +
stat_function(fun = function(x){3 + 5*x + 2*x^2}, color = "red")
``````