Question

output 20, 30, 40
input 2, 4 3,

2 can do into 20 and 40
4 can go into 40
3 can go into 30

Answer 1

does it show a function though

Answer 2

is x(3)+y(3)-3xy=0 a function or nonfunction

Answer 3

It looks like you're trying to relate some inputs to certain outputs based on divisibility. Here’s a breakdown of the relationships you've presented:

- For the output **20**:
- The input **2** can be used to divide 20 (20 ÷ 2 = 10), and it can also divide 40 in the same way (40 ÷ 2 = 20).

- For the output **30**:
- The input **3** can be used to divide 30 (30 ÷ 3 = 10).

- For the output **40**:
- The input **4** can be used to divide 40 (40 ÷ 4 = 10).
- The input **2** can also divide 40 as mentioned above.

In summary:
- **2** can be used for outputs **20** and **40**.
- **3** is specific to output **30**.
- **4** is specific to output **40**.

Would you like to explore this concept further or do you have any other questions?

Answer 4

To determine if the relationships you've outlined can be described as a function, we need to consider the definition of a function. A function associates each input with exactly one output.

In your case:

- **Input 2** can produce outputs **20** and **40**.
- **Input 3** produces output **30**.
- **Input 4** produces output **40**.

From this information, we can observe the following:

1. **Input 2** does not map to a single output since it can correspond to both **20** and **40**. This violates the definition of a function, as a function cannot assign multiple outputs to a single input.
2. **Input 3** has a single output (**30**).
3. **Input 4** has a single output (**40**).

Since input **2** can lead to multiple outputs, the overall mapping you presented does not define a function.

To clarify, if you wanted to create a function-like relationship, you would need to revise the assignments so that each input maps to only one specific output. For example, if you were to uniquely associate each number like this:

- Input 2 → Output 20
- Input 3 → Output 30
- Input 4 → Output 40

This would be a valid function, as each input corresponds to one unique output.

Answer 5

To analyze the equation \( x(3) + y(3) - 3xy = 0 \), let's first clarify its structure. The expression can be rewritten as:

\[
3x + 3y - 3xy = 0
\]

which simplifies to

\[
3(x + y - xy) = 0
\]

Dividing through by 3 (assuming \( x \) and \( y \) are not such that the denominator results in an undefined situation), we obtain:

\[
x + y - xy = 0
\]

Now, if we rearrange this equation to express \( y \) in terms of \( x \):

\[
y = \frac{x}{x - 1}
\]

This rearranged form represents \( y \) as a function of \( x \), **but** there are some important considerations:

1. **Domain Issues**: The expression \( \frac{x}{x - 1} \) is undefined when \( x = 1 \) (it leads to division by zero). So the domain of this function excludes \( x = 1 \).

2. **Inverse Behavior**: For each value of \( x \) (except for \( x = 1 \)), there is exactly one corresponding value of \( y \). This suggests that it behaves like a function.

3. **Graphical Representation**: If we were to graph the equation \( x + y - xy = 0 \), we would see a curve that potentially cuts through the plane in such a way that for most values of \( x \), there would be a single \( y \) value that corresponds.

### Conclusion:
Yes, the equation \( x + y - xy = 0 \) can be interpreted as defining \( y \) as a function of \( x \) (except at the point where \( x = 1 \)). Therefore, it defines a non-function at that specific value but can be considered a function elsewhere in its domain.