Questions: Graph the exponential function represented in the table. x -1 0 1 2 w(x) 1.5 3 6 12

Solution Steps

Given the table: \[ \begin{array}{c|c} x & W(x) \\ \hline -1 & 1.5 \\ 0 & 3 \\ 1 & 6 \\ 2 & 12 \\ \end{array} \] We need to identify the exponential function \( W(x) \).

Notice the pattern in the values of \( W(x) \):

• \( W(0) = 3 \)
• \( W(1) = 6 \)
• \( W(2) = 12 \)

The function appears to double for each increment of \( x \). This suggests the function is of the form \( W(x) = 3 \cdot 2^x \).

Verify the function \( W(x) = 3 \cdot 2^x \) with the given values:

• For \( x = -1 \): \( W(-1) = 3 \cdot 2^{-1} = 3 \cdot \frac{1}{2} = 1.5 \)
• For \( x = 0 \): \( W(0) = 3 \cdot 2^0 = 3 \)
• For \( x = 1 \): \( W(1) = 3 \cdot 2^1 = 6 \)
• For \( x = 2 \): \( W(2) = 3 \cdot 2^2 = 12 \)

The function \( W(x) = 3 \cdot 2^x \) matches all the given values.

Compare the function \( W(x) = 3 \cdot 2^x \) with the provided graphs. The correct graph should show an exponential growth starting at \( W(0) = 3 \) and doubling for each increment of \( x \).

Final Answer