Question

Please help me solve this question I do not understand how to do it. Thanks

Answer 1

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.

Answer 2

Note that for x = 0, you need f(0) = 2, so you can delete the second option.

For x = 1, you need f(1) = 4. So, the third option must to be removed.

For x = 2, you need f(2) = 8, the only that satisfies this value is the first option (between the first option and the fourth option), therefore the answer is the first option.