 # Function Tables

There are different kinds of function tables. Here, I’ll show you two types: One that is good in the beginning, when everything is kind of new, and a smaller, more professional table. A function table is a table that shows which coordinates you are plotting in the coordinate system, such that you can draw the graph of the function.

In the beginning, it might be wise to use a table like the one below. It has four columns: A column for the $x$-values you have chosen (or are told to use in the exercise), a column for calculating every value of $y$, a column for the result of the previous calculation, and a column for the coordinates you need to draw the graph. It looks like this: In the first column, I put the $x$-values. The function was $y=2x+3$ this time. I’ve put this in the second column, and replaced $x$ with the values I chose. In the third column are the $y$-values, meaning the corresponding $y$-values for each $x$ I chose. In the fourth column, I added the $x$-values and the $y$-values together into coordinates $\left(x,y\right)$. These are the coordinates you’ll insert into the coordinate system, and draw lines between to see the graph.

A more professional function table only contains exactly what you need to draw the graph of the function. The difference from the last function table is that the second and the fourth column are removed. In addition, I have written the table horizontally instead of vertically. Even if the coordinate column is not included, the $x$-values and $y$-values still are, and it’s exactly these that are the coordinates. The coordinate $\left(x,y\right)$ is there, but now it is written vertically.

 $x$-values $-5$ $-3$ $0$ $1$ $2$ $4$ $y$-values $-7$ $-3$ $3$ $5$ $7$ $11$