Functions 1

<a href="https://www.prepswift.com/quizzes/quiz/prepswift-functions-1" target="_blank">Functions 1 Exercise</a>For our introduction in Functions I, I recommend thinking of a function as a machine that takes an INPUT and then spits out an OUTPUT. Functions are equations denoted by the $f(x)$ symbol. Let's make sure we understand all of the terminology with an example. $$f(x) = x^2 +1$$ The input is what's between the parentheses. In this case, the input is simply $x$.  The output is $f(x)$, which is also equal to $x^2+1$, so both of these can be considered the output. Let's recap: <ul> <li>INPUT: $x$</li> <li>OUTPUT: Either $f(x)$ or $x^2+1$.</li> </ul> So let's imagine we start inputting values into our function machine, say $x=3$. We then get... $$f(3)=3^2 +1 = 10$$ So we have $f(3) = 10$. In other words, when the input is $3$, the output, $f(3)$, is $10$. Another Thing to Keep in Mind You can set one function equal to another. For example... $$f(x) = f(x+1)$$ What exactly is this saying? It's saying that the output of the left side of the equation, $f(x)$ is equal to the output of right side of the equation, $f(x+1)$, even when we add $1$ to the input. Remember the input is what's inside the parentheses. So let's translate... Even when we add $1$ to the input, the output remains the same. So if $f(3) = 7$, we also know that $f(4)=7$. And $f(5)$..and $f(6)$...you get the idea.