# Input-Output Tables

An
**
input-output table
**
is often used to generate a set of
ordered pairs
for a
function
, when the rule is known.

**
Example 1:
**

$x$ | $0$ | $1$ | $2$ | $3$ | $4$ |

$y=3x+1$ | $1$ | $4$ | $7$ | $10$ | $13$ |

Here, the function rule is $y=3x+1$ .

The first input is $0$ . Since $3\left(0\right)+1=1$ , the first output is $1$ .

The second input is $1$ . Since $3\left(1\right)+1=4$ , the second output is $4$ .

The $5$ ordered pairs in this table can be plotted and used to graph the equation, as shown.

Alternatively, you may be presented with an input-output table and asked to guess the rule for the function.

**
Example 2:
**

Guess the function rule.

$x$ | $10$ | $16$ | $26$ | $100$ | $200$ |

$y$ | $4$ | $7$ | $12$ | $49$ | $99$ |

With a little thought you can guess that:

$y=\frac{1}{2}x-1$

Note that for this kind of problem, you can never say for
*
sure
*
what the function rule is, since for any finite set of ordered pairs, there are many different functions that go through them. But usually there is a fairly obvious one that you can guess.