This tutorial has two parts. In the first part you’ll learn how to plot functions in R. In the second part you’ll learn how we can use R to study the Binomial random variable.

## Plotting Curves in R

You’ve already seen a number of examples of the `plot`

function in R. So far we’ve mainly plotted *points* but we can actually use the same command to plot functions. The basic idea is to set up the `x`

and `y`

coordinates of some points that are close enough together that it *looks* like we’ve plotted a smooth curve. Everything on a computer is actually discrete: your eye is simply fooled into thinking that things look continuous. All curves are actually many tiny line segments!

### Simple Example

Let’s start by plotting a few points on the curve \(f(x) = x^2\)

```
x <- seq(from = -1, to = 1, by = 0.5)
y <- x^2
plot(x, y)
```

Those points aren’t “dense” enough to approximate the whole curve. Let’s try making a finer plot:

```
x <- seq(from = -1, to = 1, by = 0.1)
y <- x^2
plot(x, y)
```

This looks better, but how about even finer?

```
x <- seq(from = -1, to = 1, by = 0.01)
y <- x^2
plot(x, y)
```

This is more like what we’re after, but we’d rather have a smooth curve rather than all those little “dots.” We can do this as follows:

`plot(x, y, type = "l")`

### Exercise #1

Plot \(f(x) = x^3\) on \([-2,2]\).

```
x <- seq(from = -2, to = 2, by = 0.01)
y <- x^3
plot(x, y, type = 'l')
```

### Exercise #2

Plot \(f(x) = \log(x)\) on \([0.5, 1.5]\).

```
x <- seq(from = 0.5, to = 1.5, by = 0.01)
y <- log(x)
plot(x, y, type = 'l')
```

### Exercise #3

Plot \(f(x) = \sin(x)\) on \([0, 6\pi]\).

```
x <- seq(from = 0, to = 6 * pi, by = 0.01)
y <- sin(x)
plot(x, y, type = 'l')
```