 So let's talk about function notation. Function notation is just a shorthand way of communicating what to do with an input or output for clearly defined variables in an equation or situation. So we have a variable or a number can be inside the parentheses. And if we're writing just a function notation like f of x equals 2x plus 4, we usually have a variable in there. But it could also be a number. And whatever's inside this parentheses is always our input, okay? Always the input. This variable and this thing always match. So you substitute into the function for the input. So we have f of x is equal to 2x plus 4. That's just our function. So f of negative 3 means that I want x to be negative 3. And if this x is negative 3, then so is the x on the other side. So I write 2 times my x, which now is negative 3 plus 4. And if I do the math, this is negative 6 plus 4, so it's equal to negative 2. It happens if I have the other kind of function notation. F of x equals y. That means that y and f of x are interchangeable. You can think of it. We usually see y equal equations, but it could very easily be an f of x equation that makes a function notation. So if the number is not inside the parentheses like the example above, then it's going to be the output value. It's going to replace f of x or y if you want to rewrite it that way. So again, our same function f of x is equal to 2x plus 4. If f of x equals 10, then that means we are going to replace f of x with 10. So 10 is equal to 2x plus 4. Notice I still have an x because in my function notation, I still have an x. So this says that y is equal to 10. So then where I would normally think of y, I'm going to put my 10. If I subtract the 4 from both sides, I get 6 is equal to 2x. If I divide by 2, x is equal to 3. Now let's try looking at a graph and see if we can look at our function notation. The key thing is to remember, is the number they give me an x or is it a y? Inside the parentheses, that's an x. And I'm trying to find the y value. So f of 0 means that x is 0. So I come to the origin and I look to see where that is on my graph. When x is 0, y is 2. Negative 2 is an x. So I look at negative 2, go to my graph to find out what the y value is. That's this point right here. So y is 6. The y is 6. The x was negative 2. Now when I look at it this way, remember f of x is equal to y. So this 4 is a y value. Okay, we have a y here. So we look at the 4 on the y-axis, go over to our graph, and see that that corresponds down here to negative 1. So x is equal to negative 1. Again, this is a y. So I go to negative 2 on my y-axis, and then go over to my graph and see that that's related to the x equaling 2. So when you don't have anything inside the parentheses, you're looking for x. You're trying to find x. So let's use an equation. We've looked at graph. Now let's look at just an equation and review how to do that. So we have f of x equals 7x plus 2, and part a is asking us for f of negative 2. So we want the f function, and wherever we see x, we're going to replace it with negative 2. So 7 times negative 2 plus 2. 7 times negative 2 is negative 14 plus 2, which will mean that this f of negative 2 is actually equal to negative 12. We have h of 5. So I want the h function over here, and wherever I see an x, I'm going to put 5. So I have 2 times 5, and that x is being squared, so I have to square my 5, minus 10. And this is 2 times 5 squared would be 25 times 2, or 50, minus 10. So h of 5 is equal to 40. And the last problem, we had this g function. Find x, such that g of x is equal to 15. So remember this is a y. So we're going to say 15 is equal to negative 1.25x plus 14. And by subtracting the 14, we get 1 is equal to negative 1.25x. And if we divide by negative 1.25, we find out that negative 0.8 is equal to x.