Questions: Construct a table of values for the function. (Round your answers to three decimal places.) f(x) = 2^(x+1) + 3 x -2 -1 0 1 2 f(x) 3.5 5 Sketch the graph of the function.

Construct a table of values for the function \( f(x) = 2^{x+1} + 3 \).

Calculate \( f(x) \) for \( x = -2 \).

\[ f(-2) = 2^{-2+1} + 3 = 2^{-1} + 3 = \frac{1}{2} + 3 = 3.5 \]

Calculate \( f(x) \) for \( x = -1 \).

\[ f(-1) = 2^{-1+1} + 3 = 2^{0} + 3 = 1 + 3 = 4 \]

Calculate \( f(x) \) for \( x = 0 \).

\[ f(0) = 2^{0+1} + 3 = 2^{1} + 3 = 2 + 3 = 5 \]

Calculate \( f(x) \) for \( x = 1 \).

\[ f(1) = 2^{1+1} + 3 = 2^{2} + 3 = 4 + 3 = 7 \]

Calculate \( f(x) \) for \( x = 2 \).

\[ f(2) = 2^{2+1} + 3 = 2^{3} + 3 = 8 + 3 = 11 \]

\[ \boxed{ \begin{array}{|c|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 \\ \hline f(x) & 3.5 & 4 & 5 & 7 & 11 \\ \hline \end{array} } \]

\[ \boxed{ \begin{array}{|c|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 \\ \hline f(x) & 3.5 & 4 & 5 & 7 & 11 \\ \hline \end{array} } \]

{"axisType": 3, "coordSystem": {"xmin": -3, "xmax": 3, "ymin": 0, "ymax": 12}, "commands": ["y = 2**(x+1) + 3"], "latex_expressions": ["$y = 2^{x+1} + 3$"]}