During Class

Brain Gains

  • In R, plot the function $f(x) = 3x$ for $-4\leq x\leq 7$.

Solution

There are many ways to do this. Here is one. 

f <- function(x){3*x}
x <- seq(-4,7,0.1)
plot(x,f(x), type = "l")
  • In R, plot the function $g(x) = -2$ for $-5\leq x\leq 5$.

Solution

Again there are many ways to do this. The following option, which tries to mimic the previous, will fail. 

f <- function(x){-2}
x <- seq(-5,5,0.1)
plot(x,f(x), type = "l")

# Error in xy.coords(x, y, xlabel, ylabel, log) : 'x' and 'y' lengths differ

Why did it fail? Because the output is $-2$ regardless of how many elements are passed into the function with the vector $x$. The output is a single number, not $-2$ for each input. This is what the error message "'x' and 'y' lengths differ" means.

One way to fix the problem above is to multiply $x$ by 0, preserving the number of elements in $x$, and then subtracting 2. 

f <- function(x){0*x -2}
x <- seq(-5,5,0.1)
plot(x,f(x), type = "l")

We can actually complete both of the above exercises with a single function, where we use $m$ and $b$ as parameters for the slope and intercept of a line, and then pass these parameters into the function. 

f <- function(x, m, b){m*x + b}
x <- seq(-4,7,0.1)
plot(x,f(x,3,0), type = "l")
x <- seq(-5,5,0.1)
plot(x,f(x,0,-2), type = "l")

Discussion - Create and Knit an RMarkdown

  • Click the New File icon OR Click File -> New File -> R Markdown
  • Knit the document, so verify you can get HTML output.
    • Typing Math
      • Not required in Math 119 (You can insert an imagine with handwritten math.)
      • But you can copy Latex from our Wiki or Project Instructions.

Practice creating HTML with RMarkdown

  • Given $h(x) = \sqrt{3-x}$, let's compute $h(-4)$ and $h(5)$ inside an R coding chunk.
  • Now let's write a cohesive analysis to explain what we're doing.
  • We'll then knit our RMarkdown file, and knit it.

Group Meeting

Start by giving each person a moment to share what they chose to prepare for class. Help each other address any questions. When each person has had a chance to share, move on the other activities.

Interactive Programming Activity

The prep for today included completing an interactive programming activity (see above). As a group, discuss each question below.

  • What does the seq() command do?
  • How does the plot() command work?
  • What does c() command do?
  • What does the <- symbol do?
  • How was the $ symbol used?
  • What does the head() command do?

Activity - RStudio Practice

Help each other use RStudio to calculate each value, by first defining a function, and then evaluating the function at various inputs. Practice putting your work in an RMarkdown file and writing a cohesive analysis to introduce each computation in a code chunk.

  • Let $w(v) = v^2 - 5v -6$ Compute the following values.
    • $w(-1)$
    • $w(-3)$
    • $w(6)$
    • $w(4)$

Answers 

w <- function(x){
x^2 - 5*x - 6
}

w(-1)
w(-3)
w(6)
w(4)

# Or all at once.
x <- c(-1,-3,6,4)
w(x)
  • Let $f(x) = \frac{2x+4}{x^2}$. Find each of the following values.
    • $f(-4)$
    • $f(1)$
    • $f(0)$

Answers 

f <- function(x){
(2*x + 4)/(x^2)
}

f(-4)
f(1)
f(0)

# Or all at once.
x <- c(-4,1,0)
f(x)

Note: Make sure you know how to interpret the output from R. The value $f(0)$ is undefined. Infinity, $\infty$, is not a number but a concept.

  • Let $f(x) = 8x^2 - 15$. Find each of the following values.
    • $f(-2)$
    • $f(1)$

Answers

Compute $f(-2)$ 

8*(-2)^2 - 15

Compute $f(1)$ 

8*(1)^2 - 15
  • Consider the piecewise function $$g(x) = \begin{cases} x^2 - 6 & \quad x < 0 \\ \\ 10 - x & \quad x \geq 0. \end{cases}.$$ Find the following values.
    • $g(7)$
    • $g(-7)$
    • $g(-33)$
    • $g(0)$

Answers 

g <- function(x){ ifelse(x < 0, x^2-6, 10-x) }

g(7)
g(-7)
g(-33)
g(0)

x <- c(7,-7,-33,0)
g(x)
  • Consider the piecewise function $$f(x) = \begin{cases} x^3 & \quad x < -1 \\ \\ -2 & \quad -1 < x < 4 \\ \\ \sqrt{x} & \quad x \geq 4. \end{cases}$$ Find the following values.
    • $f(-2)$
    • $f(-0.5)$
    • $f(3)$
    • $f(0)$
    • $f(5.2)$
    • $f(-1)$
    • $f(4)$

Answers 

f <- function(x){
  ifelse(x < -1, x^3, ifelse(
         x > -1 & x < 4, -2, ifelse(
         x >= 4, sqrt(x),
         NA)))
}

f(-2)
f(-1)
f(0)

x <- c(-2,-0.5,3,0,5.2,-1,4)
f(x)

Discussion

Prepare for our Project work

Project 1

We'll have a brief discussion about the project work, and start looking at the example project.