which table represents points on the graph of $h(x) = \sqrt3{-x} + 2$?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Function Evaluation" ], "new_concepts": [], "current_concepts": [ "Function Evaluation", "Cube Root Graphs" ] } ## Evaluate the function at key x-values $$ \begin{aligned} h(x) &= \sqrt[3]{-x} + 2 \ h(0) &= \sqrt[3]{0} + 2 = 2 \ h(1) &= \sqrt[3]{-1} + 2 = -1 + 2 = 1 \end{aligned} $$ ## Evaluate at larger x-values to distinguish tables $$ \begin{aligned} h(8) &= \sqrt[3]{-8} + 2 = -2 + 2 = 0 \ h(-8) &= \sqrt[3]{-(-8)} + 2 = \sqrt[3]{8} + 2 = 2 + 2 = 4 \end{aligned} $$ ## Match with the correct table options $$ \begin{aligned} &\text{Table 1 contains: } (-8, 4), (-1, 3), (0, 2), (1, 1), (8, 0) \ &h(-1) = \sqrt[3]{-(-1)} + 2 = 1 + 2 = 3 \ &\text{All points in Table 1 satisfy } y = h(x). \end{aligned} $$

(A) Table 1: x = [-8, -1, 0, 1, 8], y = [4, 3, 2, 1, 0]

(B) Table 2: x = [-2, -1, 0, 1, 2], y = [10, 3, 2, 1, -6]

(C) Table 3: x = [-6, 1, 2, 3, 10], y = [2, 1, 0, -1, -2]

(D) Table 4: x = [-4, -3, -2, -1, 0], y = [-8, -1, 0, 1, 8]

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Function Evaluation" ] }

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Explanation:

Evaluate the function at key x-values

Evaluate at larger x-values to distinguish tables

Match with the correct table options

Answer: