This problem involves writing functions.

Questions

Some of the exercises are not tested by Dodona (for example the plots), but it is still useful to try them.

1. Write a function, Power(), that prints out the result of raising 2 to the 3rd power. In other words, your function should compute \(2^3\) and print out the results to the console. Run the command Power() and verify if it prints 8 to the console.

   Hint: use the print() function to output the result.

2. Create a new function, Power2(), that allows you to pass any two numbers, x and a, and prints out the value of x^a to the console. You can do this by beginning your function with the line

    Power2=function(x,a){
   

   You should be able to call your function by entering, for instance,

    Power2(3,8)
   

   on the command line. This should output the value of \(3^8\), namely, 6561.
   
   

3. Using the Power2() function that you just wrote, compute \(10^3\), \(8^{17}\), and \(131^3\).
   
   

4. Now create a new function, Power3(), that actually returns the result x^a as an R object, rather than simply printing it to the screen. That is, if you store the value x^a in an object called result within your function, then you can simply return() this result, using the following line:

    return(result)
   

   The line above should be the last line in your function, before the } symbol.
   
   

5. Test your function Power3() by computing \(7^4\) using the function and assign the result to the variable power3.test. Notice that the result of \(7^4\) will only be printed to the console if you print power3.test.
   
   

6. Try to recreate the following plot:
   
   

   1. Create a numeric vector with integers ranging from -100 to 100. Store the result in x.
   2. Now using the Power3() function, create a numeric vector \(f(x) = x^2\). Store the result in y.
   3. Use the plot() function to verify that your variables x and y are correct.