SOLUTION
To tackle the problem we could try values of x and check with corresponding values of f(x)
Hence we will check for (0, f(0)) and (2, f(2)) through the options
[tex]\begin{gathered} \text{For option A} \\ \text{where x=0, f(0) = }3^0\text{ - }2\text{ }\Rightarrow\text{ 1 - 2 = -1} \\ \text{where x=2, f(2) = }3^2\text{ - }2\text{ }\Rightarrow\text{ 9 - 2 = }7 \end{gathered}[/tex]Here we see clearly that these results are not consistent with the graph
[tex]\begin{gathered} \text{For option B} \\ \text{where x=0, f(0) = 4}^0\text{ - }2\text{ }\Rightarrow\text{ 1 - 2 = -1} \\ \text{where x=2, f(2) = 4}^2\text{ - }2\text{ }\Rightarrow\text{ 16 - 2 = 1}4 \end{gathered}[/tex]Here we see clearly that these results are not consistent with the graph
[tex]\begin{gathered} \text{For option C} \\ \text{where x=0, f(0) = 4}^{0-2}\text{ }\Rightarrow4^{-2}\text{ = }\frac{1}{4^2}\Rightarrow\text{ }\frac{1}{16} \\ \text{where x=2, f(2) = 4}^{2-2}\text{ }\Rightarrow4^0\text{ = }1 \end{gathered}[/tex]Here we see clearly that these results are not consistent with the graph
[tex]\begin{gathered} \text{For option D} \\ \text{where x=0, f(0) = 4}^{0-2}+2\text{ }\Rightarrow4^{-2}+2\text{ = }\frac{1}{4^2}+2\Rightarrow\text{ 2}\frac{1}{16} \\ \text{where x=2, f(2) = 4}^{2-2}+2\text{ }\Rightarrow4^0+2^{}\text{ = }1+2\Rightarrow\text{ 3} \end{gathered}[/tex]This shows the most consistency with the graph. The answer is option D
