Question

he table below represents which type of function?
Input Output
1 4
2 8
3 12


Nonlinear Function

Linear Function

Answer 1

To determine if the function represented by the input-output table is linear or nonlinear, we can check if the relationship between the input and output values is consistent.

Let's analyze the data provided:

- For an input of 1, the output is 4.
- For an input of 2, the output is 8.
- For an input of 3, the output is 12.

Now, let's find the differences in outputs:

1. From input 1 to 2: 8 - 4 = 4
2. From input 2 to 3: 12 - 8 = 4

The differences between the outputs are constant (4), which suggests that the function is linear. A linear function can be represented by the equation of the form \(y = mx + b\), where \(m\) is the slope.

Here, you can see that the output increases by a constant amount (4) for each increase in the input (by 1), confirming that this is a linear function.

Therefore, the answer is **Linear Function**.