Considering the scatter plot.
If we are to connect the points on the points together, we cannot connect the points with a straight line. This tells us that the function can not be a linear function.
In the options, f(x) = 2x and f(x) = -2x are both linear functions. Hence, the answer can not be any of these two options.
The last option which is f(x) = 2x^2 is a quadractic function. And remember that the graph of a quadractic function is usually a curve, either opening upward (U-shaped) or opening downward (n- shaped). The scatter plot given is neither U-shaped curve or n-shaped curve, this means the answer cannot be f(x) = 2X^2
Now, we have confirmed that second, third and fourth options are cannot be the answer. Let us examine the first option.
The first option which is f(x) = 2^x is a an exponential funcion. And the shape of the plot when connected together will give a curve that resembles an exponential function. And the values when plotted on the graph correlates with f(x) = 2^x
The graph of f(x) = 2^x is shown below
Hence, in conclusion:
The correct answer is f(x) = 2^x. The first option is the correct answer