Select the correct answer
Which one of these functions is an exponential function?

A

Step-by-step explanation:

The second table

Step-by-step explanation:

When x-values are uniformly spaced (1 apart, for example), y-values are also uniformly spaced (have a common difference) when the function is linear.

The second table shows a common difference of 2 between y-values, so that function is linear.

Table 1 differences are 2, 6, 10, so is likely quadratic.

Table 3 differences are -1, -3, -5, so is likely quadratic.

Table 4 differences are 1, 3, 5, so that one, too, is likely quadratic.

Comment on differences

We call the differences between table values the "first differences." Then the differences between those are "second differences." Differences between the  "n-1-th" differences are called the "n-th" differences. When n-th differences are constant (and not zero), the table values can be represented by a polynomial of n-th degree.

Hence when 1st differences are constant, the table represents a 1st-degree (linear) function. When 2nd differences are constant, the table represents a quadratic function.