- Tables, Graphs, Functions and Sequences
- Home
- Making a table and plotting points given a unit rate
- Graphing whole number functions
- Function tables with two-step rules
- Writing a function rule given a table of ordered pairs: One-step rules
- Graphing a line in quadrant 1
- Interpreting a line graph
- Finding outputs of a one-step function that models a real-world situation
- Finding outputs of a two-step function with decimals that models a real-world situation
- Writing and evaluating a function that models a real-world situation: Basic
- Graphing ordered pairs and writing an equation from a table of values in context
- Writing an equation and drawing its graph to model a real-world situation: Basic
- Identifying independent and dependent quantities from tables and graphs
- Finding the next terms of an arithmetic sequence with whole numbers
- Finding the next terms of a geometric sequence with whole numbers
- Finding patterns in shapes

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# Writing a function rule given a table of ordered pairs: One-step rules

In this lesson, we find the function rule given a table of ordered pairs.

We first identify the input and the output variables and their values. We find if the function is increasing or decreasing.

If the function is increasing, it means there is either an addition or multiplication operation between the two variables.

If the function is decreasing, it means there is either a subtraction or division operation between the two variables.

Consider the following table −

x | y |
---|---|

3 | 15 |

5 | 25 |

6 | 30 |

8 | 40 |

9 | 45 |

We see that the y values are increasing as the x values are increasing. So it is an increasing function. So, the variables x and y must be related either by addition or multiplication operation.

We check addition operation on x and y values as follows −

3 + 12 = 15

5 + 12 = 17

We check multiplication operation on x and y values as follows −

3 x 5 = 15

5 x 5 = 25 and so on

We see that the relation between x and y is a multiplication operation here and the constant for which all values are satisfied is 5.

So the function rule for this table of x and y values is “**Multiply by 5**”.

Consider another table −

x | y |
---|---|

10 | 13 |

15 | 18 |

19 | 22 |

23 | 26 |

28 | 31 |

Here we identify the input and output and then see the output y is increasing as input x is increasing.

13 = 10 + 3; 18 = 15 + 3; 22 = 19 + 3 and so on.

So, output y = input x + 3

Therefore, we identify the function rule here as “**Add 3**”.

Given the following table of ordered pairs, write a one-step function rule.

Input(x) | Output(y) |
---|---|

0 | 3 |

2 | 5 |

4 | 7 |

6 | 9 |

8 | 11 |

### Solution

**Step 1:**

From the table 0 + 3 = 3; 2 + 3 = 5 and so on

**Step 2:**

Input + 3 = Output or x + 3 = y

**Step 3:**

Therefore the function rule here is ‘**Add 3**’ to the input to get the output.

Given the following table of ordered pairs, write a one-step function rule.

Input(x) | Output(y) |
---|---|

0 | 0 |

1 | 6 |

2 | 12 |

3 | 18 |

4 | 24 |

### Solution

**Step 1:**

From the table 0 × 6 = 0; 1 × 6 = 6 and so on

**Step 2:**

Input × 6 = Output or x × 6 = y

**Step 3:**

Therefore the function rule here is ‘**Multiply by 6**’ the input to get the output.