Which table represents a linear function?

Which table represents a linear function?

Ans. Table 2 represents a linear function.

A function is considered a linear function if it has a constant rate of change. This means that for every equal increase in the input variable x, the output f(x) increases by the same fixed amount i.e. it increases at a steady rate. We can verify this by finding the slope between each consecutive pair of points.

How to identify a linear function from a table

To check if a table represents a linear function:

1. Look at the change in x

2. Compare it with the change in f(x)

3. If the change in f(x) is constant → the function is linear

For Table 2, every time x is raised by 1 (0 to 1, 1 to 2, etc.), the value of f(x) always rises by 6 (4 to 10, 10 to 16, etc.). This is the constant change, or slope, and it informs us that Table 2 is linear. For Table 1, however, we can see that every time that x is raised by 1, the value of f(x) doubles, so it is not linear, but exponential.

Difference between Linear and Exponential

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