Question

Which of the following is the equation for this graph?

Answer 1

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

`\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}`

Here we see clearly that these results are not consistent with the graph

`\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}`

Here we see clearly that these results are not consistent with the graph

`\begin{gathered} \text{For option C} \\ \text{where x=0, f(0) = 4}^(0-2)\text{ }\Rightarrow4^(-2)\text{ = }(1)/(4^2)\Rightarrow\text{ }(1)/(16) \\ \text{where x=2, f(2) = 4}^(2-2)\text{ }\Rightarrow4^0\text{ = }1 \end{gathered}`

Here we see clearly that these results are not consistent with the graph

`\begin{gathered} \text{For option D} \\ \text{where x=0, f(0) = 4}^(0-2)+2\text{ }\Rightarrow4^(-2)+2\text{ = }(1)/(4^2)+2\Rightarrow\text{ 2}(1)/(16) \\ \text{where x=2, f(2) = 4}^(2-2)+2\text{ }\Rightarrow4^0+2^{}\text{ = }1+2\Rightarrow\text{ 3} \end{gathered}`

This shows the most consistency with the graph. The answer is option D