# Introduction to x-y graphs

## Typed out information above, in case you can't read it

Basics of X-Y Graphs

Important Conventions

- x is the horizontal axis
- y is the vertical axis
- the directions of up and right are positive
- points are represented in ordered pairs formatted (x-coordinate, y-coordinate)

Quadrants of a graph start with the quarter where both the x and y axes are positive (I) and are numbered up to IV (4) counter-clockwise.

Functions relate the x-coordinate of a point to the y-coordinate of a point. These will create lines of a whole bunch of shapes, depending on what the function actually is.

Take a look at the graphs below and think about the function they represent (visualized with the red line).

# Do these two graphs have the same function?

- Yes
- No
- I donâ€™t know
- I canâ€™t know

0 voters

## Answer spoiler

You *canâ€™t* know! So while the two of them, in reality, were drawn from the same function, only I could tell you that because I made them (using desmos.com, which I highly recommend for graphing).

In the graph, I increased how much range of the y-axis would be shown, to make the function look slightly different.

Graphs can get even more complicated than that and can have axes that grow exponentially or logarithmically in order to make data more visible or show the desired results. This often isnâ€™t something that will be used to trick you, and you can usually assume that graphs are designed *not* to be confusing or use non-linear axes if no units or values are provided.

# Drawing a function from the function or a set of data points?

This tends to be pretty easy! If youâ€™re given the function, you might already know what it looks like! If thatâ€™s the case, just draw it and skip these next steps

If you have a function you donâ€™t know anything about, plug in some values of x and y and make a table of x and y values.

Once you have a set of points, plot them on a graph. Theyâ€™ll probably start to take on a shape, especially if you get a lot of them.

Then you can draw a line connecting the points and youâ€™ll have drawn the function!

If you have the function, you can put it into a graphing calculator to *check* your work. I cannot recommend just plugging it in and drawing it, since thatâ€™s usually not whatâ€™s wanted from exercises like these.

Feel free to ask me any questions about graphing and graphs, Iâ€™ve done way more high-level math than this and have left a lot of information out of this, because itâ€™s complicated. (Some other topics could include non-linear axes, recognizing basic functions when theyâ€™re drawn, drawing basic functions, polar and parametric graphs, and other stuff like that)

Also, Iâ€™ve definitely over-complicated things, so feel free to ask me questions about anything you want more clarity on!