 Another important skill that you should have gotten in courses prior to calculus is the ability to evaluate a function. And when we define a function using our function notation, what we're actually doing is we're giving a recipe a set of instructions for what we should do to our input quantity x. So when we write f of x equals some formula, what we really mean is for f of x, what we're going to do is we're going to do something with our input variable. For example, if I have the function f of x equals x plus 5, I can read this and what this is saying is it's saying take x and add 5 to it. Or if I have g of x equals x cubed minus 2x plus 7, what this is doing is it's saying take x, cube it, there's my first step, subtract twice x, and then add 7, and that's the recipe. And the important thing here is that it's important to understand that x is actually a placeholder and by itself it has no specific meaning. I don't have to use x here. I can use any other thing that I want to to indicate that there is a place there to substitute in some value. And so for example, I can find f of x equals x squared plus 2x minus 5, find f of black square. And well, how do I do this? Well, here's an easy way to proceed. We can write down our function definition. Paper is cheap. So there's no reason not to write down our function x squared plus 2x minus 5, even though it's in the problem, just write it down. Paper is cheap. And then what we'll do next is we'll just drop out every occurrence of our variable and we'll replace them with an empty set of parentheses. Paper is cheap. Don't try to save space. f of empty set of parentheses equals no longer x, empty set of parentheses. Everything else stays squared plus 3 times empty set of parentheses minus 5. And what I have now, you can think about this as a template for how I'm going to evaluate my function. And the key here is that whatever I put in the first set of parentheses needs to go in all the sets of parentheses. So what do I want? Well, I want f of black square. So black square should go into the first set of parentheses there. And if it's in the first set of parentheses, it should be in all the sets of parentheses. So I'll put it in here and I'll put it in the last one. And there's my f of black square is this thing. Well, what about some other algebraic expression? So here's f of x equals square root x squared plus 4x minus 1. And I want to find f of x plus h. So again, we can set up our template. We're going to drop the x and replace it with an empty set of parentheses. Paper is cheap. Go ahead and take up space. f of empty set of parentheses equals square root of empty set of parentheses squared plus 4 times empty set of parentheses minus 1. And the rest of those don't change. So wherever I saw an x, I'm just replacing with an empty set of parentheses. And paper is cheap. I'll copy that down again. Whatever I put in one of them is going to go in all of them. So I want an x plus h in here, which means I need to put an x plus h in here and in here. And I may have to do a little bit more algebra after this, but this is the starting point for evaluating functions.