Given the following table, what would the value of \( a \) and \( b \) be if the table:
\( \begin{array}{|c|c|c|c|} \hline \textbf{x} & \text{-}2 & \text{-}1 & 0 \\ \hline \textbf{f(x)} & a & b & 2 \\ \hline \end{array} \)
a) Was displaying a linear relationship with a common difference of \( 0.5 \)?
b) Was displaying exponential growth with a common ratio of \( 2 \)?
c) Was displaying exponential decay with a common ratio of \( 0.5 \)?
\( \begin{array}{|c|c|c|c|} \hline \textbf{x} & \text{-}2 & \text{-}1 & 0 \\ \hline \textbf{f(x)} & a & b & 2 \\ \hline \end{array} \)
a) Was displaying a linear relationship with a common difference of \( 0.5 \)?
b) Was displaying exponential growth with a common ratio of \( 2 \)?
c) Was displaying exponential decay with a common ratio of \( 0.5 \)?