A math function table is a table used to plot possible outcomes of a function, which is a kind of rule. The table results can usually be used to plot results on a graph. To fully understand function tables and their purpose, you need to understand functions, and how they relate to variables. Once you understand each piece of the puzzle, mastering functions and function tables will be a snap.
To understand functions, you first need to understand variables. A variable is a value (usually a number) that you don't know or that could be a bunch of different numbers. For example, let's say you just took a test. You're not sure what you got yet, so you refer to your grade only as "x."
A few days later the test gets handed back. You got an 83. In your case, x = 83. For your friend, x might equal 97.
A function is a rule that applies to a variable. Let's say everybody (except your friend) did poorly on the test, and your teacher decides to use a curve to change all the grades. The rule he uses for the curve is to bump everybody's grade up by 3 points. Written as a function, that would look like this:
curve(grade) = grade + 3
Or, in math-speak, you can call the curve "f" (for "function") and grade "x":
f(x) = x + 3
Now you can plug your and your friend's grades into the function to figure out what your new grades will be:
f(83) = 86 f(97) = 100
Function tables are simply lists of possible values of a variable and the function's result. Pictured is a simple function table that lists a series of possible grades in the class and then applies the f(x) = x + 3 function to them.
To create a function table, simply list a bunch of values in the left column. The values can be anything; if you're not given specific values to use, just create your own. Since you'll often be using the data on a function table for graphing (see the next section), when you can choose the values yourself, it's best to use values for "x" that are close to zero: -2, -1, 0, 1, and 2, for example.
Graphing Function Tables
The purpose of creating functions is usually to plot a graph. When you plot a graph, the "x" values will be where a point exists on the x-axis (the horizontal axis), while the "f(x)" values will be where a point exists on the y-axis (vertical). To illustrate this point, the accompanying picture displays a graph plotted using the information in the function table above.
On the graph, the original grades appear on the x-axis, and are matched to the curved grades that appear on the y-axis. Sometimes graphs can convey information that wasn't apparent before. For example, in this case, the graph proves that the grading curve was fair: no grade was raised disproportionately to any other grade. f(x) = x + 3 is obviously a very simple function, but with more advanced functions, the information might not be so obvious.
Domain and Range
When dealing with functions and plotting graphs, two important vocabulary terms to remember are "domain" and "range." "Domain" refers to the "x" value, and "range" refers to the "y" or "f(x)" value.
For example, in the function table above, the left column could be labeled "Domain" and the right column could be labeled "Range." In the graph above, the x-axis displays the domain values, while the y-axis displays the range values.