R Week 1 HomeWork

Ian Costello

Question 1

Write a loop that calculates 12-factorial

First, I created a function and assigned “y” for a number “n.” Assigned initial value “x” for loop as 1. Factorials can only be non-zero positive integers, with the lowest value as 1. I then wrote a loop for the range 1:n, where “n” is user-defined later. As the loop iterates, it multiplies x by i, which is each number in the defined range, starting with 1 * 1, until reaching the n’th number.

y <- function (n) {
        x <- 1
        for (i in 1:n) {
                x <- x * i
                }
        return(x)
}  
y(12)

## [1] 479001600

Question 2

Show how to create a numeric vector that contains the sequence from 20 to 50 by 5.

From additional quiz question 11, using the sequence function, “sec.” Syntax: starting value, ending value, interval.

seq(20,50,5)

## [1] 20 25 30 35 40 45 50

Quesiton 3

Create the function “quadratic” that takes a trio of input numbers a, b, and c and solve the quadratic equation. The function should print as output the two solutions.

Using the quadratic formula:

\(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\)

First, created a function named “quadratic.” I provided the function with three arguments for input, “a”,“b”, and “c.” Taking careful note of the order of operations, I wrote out the formula. The most difficult aspect of this problem was how to produce both solutions. After a bit of searching, I found an example of creating two separate lines for the “plus” solution and the “minus” solution. After a bit more digging, I found a really elegant solution to use “combine,” since the code will iterate automatically for all values in the vector.

quadratic <- function(a,b,c){
  x = (-b + (c(-1,1)*sqrt(b^2-4*a*c)))/(2*a)
  return(x)
}
quadratic(2,4,-30)

## [1] -5  3