1.7 R as a Graphing Calculator

stat_function() in ggplot2 allows us to visualize mathematical functions. We’ll use anonymous functions with it to create various types of plots.

First, attach the tidyverse to your current session (which includes ggplot2):

library(tidyverse)

Then use theme_set() to set a ggplot2 theme for this document. theme_minimal() is a nice, minimalist alternative to the ggplot default. Try replacing theme_minimal() with:

theme_bw() for a white background with gridlines, often used for publications.
theme_dark() for a dark background with contrasting gridlines, suitable for presentations.
theme_classic() for a minimalistic theme with only axis lines and no gridlines.
theme_void() which removes all elements (axes, gridlines, background), ideal for maps or minimal visuals.
theme_linedraw() for a clean, black-and-white theme with thin lines, designed for technical drawings.

theme_set(theme_minimal())

Example: Plot the function \(y = 2x + 1\) in red:

ggplot() +
  stat_function(fun = function(x) 2 * x + 1, color = "red")

Notice that I used an anonymous function to define the line. The function takes x as input and returns 2 * x + 1 as output.

1) Plot the line y = -3x + 6 in blue.

Multiple functions can be plotted on the same graph by adding more stat_function() layers:

ggplot() +
  stat_function(fun = function(x) 2 * x + 1, color = "red") +
  stat_function(fun = function(x) -x + 3, color = "blue")

2) Create a plot showing three lines. Choose three different colors for your plot. You can see R’s color options by running the function `colors()`, or by visiting this site: https://r-charts.com/colors/

\[\begin{align} y &= 2x + 1\\ y &= -x + 3\\ y &= 0.5x - 1\\ \end{align}\]

Controlling the Viewing Window

Use xlim() and ylim() layers to zoom in or out, controlling what portions of the function you see:

ggplot() +
  stat_function(fun = function(x) 2 * x + 1, color = "red") +
  xlim(-5, 5) +
  ylim(-10, 10)

Warning: Removed 5 rows containing missing values or values outside the scale range
(`geom_function()`).

3) Plot \(y = x^2\) showing only x-values from -3 to 3 and y-values from 0 to 10.

Polynomial Functions

You can use stat_function to plot polynomials of any degree. Here are examples of constant, linear, quadratic, and cubic functions. I use aes() in sort of a hack-y way to color and label the lines by mapping line color to different character strings (there’s no data):

ggplot() +
  stat_function(fun = function(x) 3, aes(color = "constant")) +
  stat_function(fun = function(x) 3 * x, aes(color = "linear")) +
  stat_function(fun = function(x) 3 * x^2, aes(color = "quadratic")) +
  stat_function(fun = function(x) 3 * x^3, aes(color = "cubic")) +
  xlim(-2, 2)

4) Plot these three quadratic functions:

\[\begin{align} y &= x^2\\ y &= x^2 + 2\\ y &= 2 x^2 \end{align}\]

Use different colors for each and set appropriate viewing windows.

Adding Plot Features

Add a title and axis labels to make your plots more informative using the labs() function:

ggplot() +
  stat_function(fun = function(x) x^2, color = "red") +
  xlim(-3, 3) +
  ylim(0, 10) +
  labs(title = "Quadratic Function",
       x = "x",
       y = "f(x)")

5) Plot a circle with radius 2 centered at the origin. Add a title and axis labels.

Hint: You’ll need to plot the upper and lower half separately using y = ± sqrt(4 - x^2). And to make the plot print to the document with the same height and width, use these chunk options: fig.width=6, fig.height=6