Me solve this question i do not understand how to do it.

The points are (0,2), (1,4), (2,8)

Notice that as x increases from 0 to 1 (a change of +1), y increases from 2 to 4 (a change of +2).   If this were a linear function, the slope would be 4.

As x increases from 1 to 2 (a change of +1), y increases from 2 to 4 (a change of +2).   If this were a linear function, the slope would be 2.

But as x increases from 2 to 3 (a change of +1), y increases from 4 to 8 (a change of +8).  If this were a linear function, the slope would be 4.

Thus, the slope of the graph is not uniform and the function therefore cannot be linear.  We  reject f(x) = 4x and f(x) = 2x + 2.

Now let's check out f(x) = 2(2)^x:  f(0) = 2; f(1) = 4; f(2) = 8.  This agrees with the data.

Let's also check out f(x) = x^2+2.  f(0) = 2; f(1) = 3; f(2) = 6.  This definitely does not match the given data.

The correct answer is the first one:  f(x) = 2(2)^x.

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step-by-step explanation: