# Lesson 10

Interpreting Inputs and Outputs

- Let’s look at inputs and outputs of a function.

### 10.1: A Function Riddle

The table shows inputs and outputs for a function. What function could it be?

input | output |
---|---|

1 | 3 |

2 | 3 |

3 | 5 |

4 | 4 |

5 | 4 |

10 | 3 |

11 | 6 |

### 10.2: What’s the Input?

- For each pair of variables, which one makes the most sense as the input? When possible, include a reasonable unit.
- The number of popcorn kernels left unpopped as a function of time cooked.
- The cost of crab legs as a function of the weight of the crab legs.
- \(f(t) = 5t + 8\) where \(t\) represents the time that a bike is rented, in hours, and \(f(t)\) gives the cost of renting the bike.
- \(g(n) = 7n+4\) where \(n\) represents the number of pencils in a box and \(g(n)\) represents the weight of the box of pencils in grams.

- Write the equation or draw the graph of a function relating the 2 variables.
- Input: side length of a square, output: perimeter of the square
- Input: time spent walking (minutes), output: distance walked (meters)
- Input: time spent working out (minutes), output: heart rate (beats per minute)

### 10.3: Matching Possible Inputs

For each function in column A, find which inputs in column B could be used in the function. Be prepared to explain your reasoning for whether you include each input or not.

- Take turns with your partner to match a function with its possible inputs.
- For each function, explain to your partner whether each input is possible to use in the function or not.
- For each input, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.

- \(f(\text{person}) = \text{the person’s birthday}\)
- \(g(x) = 2x + 1\)
- \(h(\text{item}) = \text{the number of chromosomes in the item}\)
- \(P(\text{equilateral triangle side length}) = 3 \boldcdot (\text{side length})\)
- \(C(\text{number of students}) = 9.99 (\text{number of students}) + 15\)

- Martha Washington (the first First Lady of the United States)
- an apple
- 6
- 9.2
- 0
- -1

For each function, write 2 additional inputs that make sense to use. Write 1 additional input that does not make sense to use. Be prepared to share your reasoning.