table
x f(x)
-2 0.2
-1 0.4
0 0.8
1 1.6
2 3.2
Look that the pair of data (0, 0.8), it means f(0) is 0.8
Given that a^0 = 1, means that the coefficient of the function has to be 0.8 and you discard the first and the third options.
You have to replace the values of x in the equations and compare the results.
For f(x) = 0.8 * (2^x) you get
x f(x) = 0.8 * (2^x)
-2 0.8 * (2^-2) = 0.8 / 4 = 0.2
-1 0.8 * (2^-1) = 0.8 / 2 = 0.4
0 0.8 * (2^0) = 0.8 * 1 = 0.8
1 0.8 * (2^1) = 0.8 * 2 = 1.6
2 0.8 * (2^2) = 0.8 * 4 = 3.2
As you can see these results are the same of the table of the question, so the function is f(x) = 0.8 (2^x).
Answer: f(x) = 0.8 * (2^x)