Answer: B.Explanation:1. Understand the function definition: The function is $f(x) = -10(2)^{\dfrac{x}{3}}$. We need to find a table that correctly lists four pairs of $x$ and their corresponding $f(x)$ values.

2. Evaluate $f(x)$ for the x-values given in the tables (typically $-3, 0, 3, 6$): - For $x = -3$: $f(-3) = -10(2)^{\dfrac{-3}{3}} = -10(2)^{-1} = -10 \times \dfrac{1}{2} = -5$. - For $x = 0$: $f(0) = -10(2)^{\dfrac{0}{3}} = -10(2)^0 = -10 \times 1 = -10$. - For $x = 3$: $f(3) = -10(2)^{\dfrac{3}{3}} = -10(2)^1 = -10 \times 2 = -20$. - For $x = 6$: $f(6) = -10(2)^{\dfrac{6}{3}} = -10(2)^2 = -10 \times 4 = -40$.

3. Examine the tables provided in the options (based on PDF page 38): [A] x | -3 | 0 | 3 | 6 -----|----|---|-----|----- f(x) | -5 | 0 | -20 | -40 (Incorrect, $f(0)$ should be $-10$)

[B] x | -3 | 0 | 3 | 6 -----|----|-----|-----|----- f(x) | -5 | -10 | -20 | -40 (Correct: matches all calculated values)

[C] x | -3 | 0 | 3 | 6 -----|----|-----|-----|----- f(x) | 5 | -10 | -20 | -40 (Incorrect, $f(-3)$ should be $-5$)

[D] (The table from snippet source 362) x | -3 | 0 | 3 | 6 -----|----|-----|-----|----- f(x) | -5 | -10 | -20 | -30 (Incorrect, $f(6)$ should be $-40$)

4. Conclusion: Table B correctly gives four values of $x$ and their corresponding values of $f(x)$ for the given exponential function. The table for option B is: x | f(x) -----|------ -3 | -5 0 | -10 3 | -20 6 | -40