Questions

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

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