I like to think of input and output like coordinates on a graph. So, the input is also called domain, and is also the x coordinate on a graph. The output is also called the range, and is also the y coordinate. For example, in the coordinate (5,7), 5 would be the input, and 7 would be the output.
Now for relation and function. A function is where each x, or the input, can only be assigned to one y: but this is where it gets a little tricky. Although an x value can only be assigned to one y, and y value can be assigned to multiple x's. Let's say for the x values you have 3 and 8, and for your y values you have 7 and 4. 3 can't be assigned to both of these, however, both 3 and 8 could be assigned to the same y. (feel free to ask me for more clarification on this, I know it's a little hard to remember). For relation, it's the opposite of what I just explained. The x values can be assigned to as many of the y values they want. For example, with the last numbers, 3 could be assigned to both 7 and 4 at the same time.
Again, feel free to ask me for more clarification, I'm just trying to keep this from sounding really complicated. I hope I helped! :)
Explanation: The diagonals of a parallelogram bisect each other. This means that the portion marked x+4 is the same length as the portion marked 2x-7; this gives us the equation x+4=2x-7.
