# Putting It Together: Function Basics

At the beginning of the module, you were considering Galileo’s famous experiment in which he dropped, or thought about dropping, two balls of different masses from the top of the Tower of Pisa. And you looked at data describing a falling object. Now that you learned about functions, let’s take another look at the data.Time (s) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

Velocity (m/s) | 0 | 9.8 | 19.6 | 29.4 | 39.2 | 49.0 | 58.8 | 68.6 | 78.4 |

Distance (m) | 0 | 4.9 | 19.6 | 44.1 | 78.4 | 122.5 | 176.4 | 240.1 | 313.6 |

*Chart shows the correlation between time (seconds 1-8), velocity and distance.*

{(0, 0), (1, 9.8), (2, 19.6), (3, 29.4), (4, 39.2), (5, 49.0), (6, 58.8), (7, 68.6), and (8, 78.4)}

Is the relation a function? Indeed it is. Each input value corresponds to only one output value. Now consider the set of ordered pairs relating time to distance.{(0, 0), (1, 4.9), (2, 19.6), (3, 44.1), (4, 78.4), (5, 122.5), (6, 176.4), (7, 240.1), and (8, 313.6)}

As before, this relation is also a function. Now that you know that both velocity and distance can be described by functions, you can evaluate them from the table.- Suppose velocity as a function of time is represented as [latex]V(t)[/latex]. Evaluate and explain [latex]V(4)[/latex]. To evaluate, find the value of the function at 4 seconds. At 4 seconds, velocity is 39.2 m/s. Therefore, [latex]V(4)=39.2[/latex].

- Similarly, solve for [latex]t[/latex] when [latex]V(t)=49.0[/latex]. Find 49.0 m/s on the table and read the related time, 5 s. That means that the velocity is 49.0 m/s after 5 seconds so [latex]V(5)=49.0[/latex].

- Suppose now that the distance is represented as [latex]D(t)[/latex]. Evaluate and explain [latex]D(6)[/latex]. To evaluate, find the value of the function at 6 seconds. It is 176.4 m, which means that the falling object travels 176.4 m in 6 seconds.

- We can also solve [latex]D(t)=240.1[/latex]. Find 240.1 m in the table and read the related time, which is 7 seconds. So [latex]D(7)=240.1[/latex].

^{2}.

[latex]V(t)=at[/latex] | [latex]D(10)={\Large\frac{1}{2}}at^2[/latex] |

[latex]V(10)=a(10)[/latex] | [latex]D(10)={\Large\frac{1}{2}}a(10)^2[/latex] |

[latex]V(10)=(9.8)(10)[/latex] | [latex]D(10)={\Large\frac{1}{2}}(9.8)(10)^2[/latex] |

[latex]V(10)=98[/latex] | [latex]D(10)=490[/latex] |

Time (s) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 10 | 13 |

Velocity (m/s) | 0 | 9.8 | 19.6 | 29.4 | 39.2 | 49.0 | 58.8 | 68.6 | 78.4 | 98 | 127.4 |

Distance (m) | 0 | 4.9 | 19.6 | 44.1 | 78.4 | 122.5 | 176.4 | 240.1 | 313.6 | 490 | 828.1 |

*Chart shows the correlation between time (seconds 1-8, 10 and 13), velocity and distance.*

## Licenses & Attributions

### CC licensed content, Original

- Putting It Together: Function Basics.
**Authored by:**Lumen Learning.**License:**CC BY: Attribution. - Input vs Output (1).
**Authored by:**Christine Caputo for Lumen.**License:**CC BY: Attribution. - Input vs Output (2).
**Authored by:**Christine Caputo for Lumen.**License:**CC BY: Attribution.