Algebra Graphing: How To Move A Graph Up Down And Change Its Slope
The Function y=x is the same as as f(x)=x. f(x) just stands for 'The Function of x'. This is to show that when you have an input (x), you get an output of that which is y. Because the coefficient for this function is 1/1, that means the slope is 1/1; in other words, to get from one point to another on the line, you would need to rise 1 point and run 1 point. To be shown as a graph, you can see that because there was no number added or subtracted from the function f(x)=x, that means the number added is really +0. So that tells us that y-intercept is (0,0), or the origin.
To make this graph move up you would need to add a number greater than 0. Whether that number is 1, or 10, or even 100, all the points on this line would shift up that amount. To make the graph move down, you would need to subtract a number, how ever many units you would like it to move down and subtract that from the original equation. This is also called a vertical shift. As you can see in the graph below, the slope of this function is 2/1. So to get from one point to another you need to move up 2, and run 1. Because the number at the end is a -3, that means the y-intercept is at (0,-3), and the whole line moves down three units from it's original function f(x)=2x.
These are just a few of the things you can do to a function, and as you move on to higher level math classes, you will learn how to make a quadratic function and many others move up, down, shift to the right, left, make the functions wider or thinner, and so much more. But for now, I hope this satisfies you!