When the input is 0, the output is 0. As the input increases by 1, the output increases by 6.
0 | 0
1 | 6
2 | 12
OR
0 | 0
1 | 6
2 | 36
The answer is the first choice because:
0 * 6 = 0
1 * 6 = 6
2 * 6 = 12
Based on the given information, there are two possible interpretations:
1. Assuming a linear relationship:
If the output increases by 6 each time the input increases by 1, then the relationship can be expressed by the equation: output = 6 * input.
Using this equation, we can calculate the output for different input values:
When the input is 0, the output is 6 * 0 = 0.
When the input is 1, the output is 6 * 1 = 6.
When the input is 2, the output is 6 * 2 = 12.
Therefore, the correct table would be:
0 | 0
1 | 6
2 | 12
2. Assuming a nonlinear relationship:
If the output increases by multiplying the input value by 6 each time, then the relationship can be expressed by the equation: output = input^6.
Using this equation, we can calculate the output for different input values:
When the input is 0, the output is 0^6 = 0.
When the input is 1, the output is 1^6 = 1.
When the input is 2, the output is 2^6 = 64.
Therefore, the correct table would be:
0 | 0
1 | 1
2 | 64.
To determine the pattern and relationship between the input and the output, we can examine the given examples:
If we consider the first example, we can observe that when the input is 0, the output is also 0. As the input increases by 1, the output increases by 6. This means that for every increase in the input by 1, the output increases by 6. For example, when the input is 1, the output is 6; when the input is 2, the output is 12.
From this pattern, we can conclude that the relationship between the input and the output can be expressed as:
output = 6 * input
In other words, the output is obtained by multiplying the input by 6.
Now, let's consider the second example, where the output for input 2 is 36. This example follows a different pattern.
In this case, we can observe that the output is obtained by squaring the input and then multiplying it by 6. For example, when the input is 2, the output is (2^2) * 6 = 36.
Therefore, the relationship between the input and the output in the second example can be expressed as:
output = 6 * (input^2)
In summary:
First example: output = 6 * input
Second example: output = 6 * (input^2)
Note that without additional examples or context, it is impossible to determine which pattern is correct. You would need more data points to make an accurate conclusion.