Question
Determine if the relationship describes a function.
Is the length of a movie a function of have many actors it has?
Number of actors Movie length (hr)
? ?
The movie length
of the number of actors.
Great job!
Try another one. Is the amount of milk in pints a function of the amount of milk in gallons? Keep in mind, there are 8 pints in 1 gallon.
Number of gallons Number of pints
? ?
The number of pints
of the number of gallons.
Great job!
What rule can we use to get from an input in gallons to an output in pints? Keep in mind, there are 8 pints in a gallon.
Number of gallons
Input Output Arrow
Input Output Arrow
Number of pints
Number of gallons Number of pints
? ?
add 8
multiply 8
divide by 8
Is the length of a movie a function of have many actors it has?
Number of actors Movie length (hr)
? ?
The movie length
of the number of actors.
Great job!
Try another one. Is the amount of milk in pints a function of the amount of milk in gallons? Keep in mind, there are 8 pints in 1 gallon.
Number of gallons Number of pints
? ?
The number of pints
of the number of gallons.
Great job!
What rule can we use to get from an input in gallons to an output in pints? Keep in mind, there are 8 pints in a gallon.
Number of gallons
Input Output Arrow
Input Output Arrow
Number of pints
Number of gallons Number of pints
? ?
add 8
multiply 8
divide by 8
Answers
GPT-4o mini
Let's break it down step by step.
### Is the length of a movie a function of how many actors it has?
- **Analysis**: In a typical context, the length of a movie is not necessarily determined solely by the number of actors. Different movies with different numbers of actors can have varying lengths. For example, a movie can have a single actor or many actors and still be a short or long film. Therefore, the relationship does not describe a function.
**Conclusion**: No, the length of a movie is not a function of the number of actors.
---
### Is the amount of milk in pints a function of the amount of milk in gallons?
- **Analysis**: Since there are 8 pints in 1 gallon, for every gallon you have, you can directly calculate the number of pints by multiplying the number of gallons by 8.
**Conclusion**: Yes, the amount of milk in pints is a function of the amount of milk in gallons.
---
### What rule can we use to get from an input in gallons to an output in pints?
- Based on the given relationship (8 pints in 1 gallon), the conversion rule from gallons to pints is to multiply by 8.
### Table Representation
You may represent the input/output as follows:
| Number of Gallons | Number of Pints |
|-------------------|-----------------|
| 1 | 8 |
| 2 | 16 |
| 3 | 24 |
| 4 | 32 |
| ... | ... |
In the table above, for every gallon, you multiply by 8 to get the number of pints.
### Input Output Arrow Representation
Here's how it would look using arrows:
- **Input**: Number of gallons → **Output**: Number of pints
- **Rule**: Multiply by 8
So if you have:
- 1 gallon → 8 pints (1 * 8 = 8)
- 2 gallons → 16 pints (2 * 8 = 16)
- 3 gallons → 24 pints (3 * 8 = 24)
And so forth.
In summary:
- **Rule**: Multiply the number of gallons by 8 to get the number of pints.
- You can express this as:
- If \( g \) = number of gallons, then \( p = 8g \) where \( p \) = number of pints.
### Is the length of a movie a function of how many actors it has?
- **Analysis**: In a typical context, the length of a movie is not necessarily determined solely by the number of actors. Different movies with different numbers of actors can have varying lengths. For example, a movie can have a single actor or many actors and still be a short or long film. Therefore, the relationship does not describe a function.
**Conclusion**: No, the length of a movie is not a function of the number of actors.
---
### Is the amount of milk in pints a function of the amount of milk in gallons?
- **Analysis**: Since there are 8 pints in 1 gallon, for every gallon you have, you can directly calculate the number of pints by multiplying the number of gallons by 8.
**Conclusion**: Yes, the amount of milk in pints is a function of the amount of milk in gallons.
---
### What rule can we use to get from an input in gallons to an output in pints?
- Based on the given relationship (8 pints in 1 gallon), the conversion rule from gallons to pints is to multiply by 8.
### Table Representation
You may represent the input/output as follows:
| Number of Gallons | Number of Pints |
|-------------------|-----------------|
| 1 | 8 |
| 2 | 16 |
| 3 | 24 |
| 4 | 32 |
| ... | ... |
In the table above, for every gallon, you multiply by 8 to get the number of pints.
### Input Output Arrow Representation
Here's how it would look using arrows:
- **Input**: Number of gallons → **Output**: Number of pints
- **Rule**: Multiply by 8
So if you have:
- 1 gallon → 8 pints (1 * 8 = 8)
- 2 gallons → 16 pints (2 * 8 = 16)
- 3 gallons → 24 pints (3 * 8 = 24)
And so forth.
In summary:
- **Rule**: Multiply the number of gallons by 8 to get the number of pints.
- You can express this as:
- If \( g \) = number of gallons, then \( p = 8g \) where \( p \) = number of pints.