Input and output tables are diagrams used to teach the basic concepts of functions. They are based on the rule of the function. When the table is filled in, it produces the pairs of coordinates that are necessary to construct the graph. The input is the value of x that is applied to the function. The output is the f(x), or the answer that is received as a result of putting x into the function.

Describe how input and output tables are useful for representing mathematical functions. Unlike regular algebraic equations, most functions are represented with f(x) rather than y. This demonstrates that f is a function of x. For every x, there is only one f(x). The input and output table helps to simplify this.

Write the outline for the input and output table. An input and output table is composed of two columns. The input column is typically on the left, and the output column is on the right. The input column is the x, and the output column is the f(x). For example, the values in the input column may be 1, 2 and 3. You will need to determine the output for each of these values.

Examine the function, and put each value of the input into the function. For example, the function may be f(x) = 2x + 4. If you put x = 1 into the function, then you will receive an answer of f(x) = 6 for the output.

Use the values in the input and output table to create a graph of the function. The graph of the function will help you to better understand the equation of the function. Plot each point of the table and then connect the points.

Use the vertical line test to prove that the function is truly a function. A relation can have an element of the input give you more than one output. Yet in a function, there is only one output for every input. Two points on the graph that form a vertical line represent a relation, but not a function. Since the points for the function f(x) = 2x + 4 fail the vertical line test, the function is valid.