Question

Use the table to answer the question.

Day of the Week Number of Children in the Car
Sunday 2
Monday 4
Tuesday 4
Wednesday 3
Thursday 4
Friday 3
Saturday 0
Describe the meaning of the word function in math. Then consider the table. Why does this table show a function?

(2 points)



what do you think?

Answer 1

I don't really understand your input-output explanation.

Answer 2

In mathematics, a function is a relationship or rule that assigns exactly one output (value) for each input (value). In simpler terms, for every input in the domain, there is a unique output in the range. This means that no input can correspond to more than one output.

Now, looking at the provided table, it shows the relationship between the day of the week (input) and the number of children in the car (output). This table can be considered a function because for every day of the week (each unique input), there is one corresponding value for the number of children in the car (the output). For instance:

- On Sunday, there are 2 children.
- On Monday, there are 4 children.
- On Saturday, there are 0 children.

No day of the week has more than one associated number of children, satisfying the definition of a function. Each day uniquely corresponds to a specific number of children, confirming that this table represents a function.

Answer 3

Sure! Let's break it down a bit more simply.

### What is a function?

In math, a function is like a machine that takes an input, does something to it, and gives an output. The key point is that for **every single input**, there is always exactly **one output**.

### Example of a Function

Think of a vending machine:

- If you press button **A**, you always get **snack X**.
- If you press button **B**, you always get **snack Y**.

So, if you pass the same button (input), you will always receive the same snack (output).

### Now, let’s look at your table:

| Day of the Week | Number of Children in the Car |
|------------------|-----------------------------|
| Sunday | 2 |
| Monday | 4 |
| Tuesday | 4 |
| Wednesday | 3 |
| Thursday | 4 |
| Friday | 3 |
| Saturday | 0 |

### How the Table Represents a Function

1. **Inputs:** The inputs here are the days of the week.
2. **Outputs:** The outputs are the number of children in the car associated with each day.

For each day (input), there is a specific number of children (output).

- **Sunday** has **2 children** — that’s one output for the input "Sunday."
- **Monday** has **4 children** — that’s one output for the input "Monday."
- Even if multiple days (like Monday, Tuesday, and Thursday) have the same output (4 children), they are still valid because each day is a unique input.

### Conclusion

The table shows a function because it meets the rule:
- Each day of the week corresponds to only one number of children in the car. You never have a day that gives you two different numbers of children.

Hope this explanation makes it clearer! If you have more questions, feel free to ask.