p3-intro-functions.md

Introduction to Functions

Before getting started, make sure that you're familiar with Sublime Text. Make sure you download a new project for today's lesson (explained in the previous link).

Lesson

Slides

Exercises

Basic Requirements

1. In the console on the blank index.html page, try the following and verify that the results match your expectations:

   square(10) + 2;
   square(100) + square(77);
   square(8 / 2)
   square(2 + 17);
   square(square(15));

2. Write a sentence in plain English describing how square(square(15)) is evaluated.

3. Rename the parameter to square in your main.js file to monkey, and rename the uses of that parameter in the body to monkey as well. Will the function square still work? Why or why not?

4. What is wrong with the following definitions of square? Write a sentence or two describing the issue(s); then, try copying the erroneous examples into a console one-at-a-time and observing the error(s) generated (you may have to attempt to invoke the functions to see the error). What errors are produced (if any) for each erroneous version? Do the errors make sense?

   function square(monkey) {
     return x * x;
   }
   
   function square(5) {
     return 5 * 5;
   }
   
   function square("x") {
     return "x" * "x";
   }

5. Fix the invalid syntax in the following functions (you can copy and paste these invalid definitions into main.js and then edit them there):

   func square1(x {
     return x * x;
   }
   
   functionsquare2 x)
     return x * x;
   }
   
   function (x) square3 {
     return x * x;

6. The following functions exhibit poor style -- fix these issues using the original version of square as a reference.

   function square(x){return x*x;}
   
   function square (x) { return x *x;
   }
   
   function square(x)
   {
   return x * x;
   }

7. Complete the function cube that returns the cube of x:

function cube(x) {
  // your code here
}

8. Complete the function fullName that should take two parameters, firstName and lastName, and returns the firstName and lastName concatenated together with a space in between.

// don't forget the parameters!
function fullName() {
  // your code here
}
fullName("John", "Doe") // => "John Doe"

9. Write a function average that takes two numbers as input (parameters), and returns the average of those numbers.

10. Write a function greeter that takes a name as an argument and greets that name by returning something along the lines of "Hello, <name>!"

11. Using the document found at this link, translate the first page of geometric formulas into JavaScript functions.

    As an example, a function to compute the perimeter of a rectangle might look like this:

    function perimeterRect(l, w) {
      return 2 * (l + w);
    }

    NOTE: JavaScript provides some nifty mathematical functions and constants built into the language that you'll need for this exercise. The two that we'll be making use of are:

    Math.PI; // => 3.141592653589793
    Math.sqrt(256); // => 16

    To test your answers, you'll need to:

    1. Save the JavaScript file that you enter your code into,
    2. Reload the corresponding index.html file (the one in the same directory as the main.js file that your code is in),
    3. Call the function with arguments in the console to see the result, e.g. perimeterRect(2, 6).
    4. Eventually, you may want to verify that the output is correct. Google is a great tool for this:

    

More Practice

Translate the rest of the geometric formulas found here into JavaScript functions.

Advanced

1. Compound interest can be calculated with the formula:

   

   • F: future value
   • P: present value
   • i: nominal interest rate
   • n: compounding frequency
   • t: time

Write a function futureValue that can be used to calculate the future value of a quantity of money using compound interest.

Use the function to calculate what the future value of $1700 (P = 1700) deposited in a bank that pays an annual interest rate of 4.7% (i = 0.047), compounded quarterly (n = 4) after 6 years (t = 6) (you can use Math.pow to do exponentiation).

2. Write a power function that accepts the parameters base and exponent and returns the result. Replace square and cube with the power function you just wrote. Do not use Math.pow.

3. Write your own square-root function called sqrt that accepts a number parameter and returns an approximate square root. Square-root approximations make use of averages. Be sure to use the average function you previously wrote. The first version of your square root function should perform no more than 3 successive averages.