which table represents a nonlinear function?

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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": [ "Rate of Change Analysis" ], "new_concepts": [ "Linear vs Nonlinear Functions" ], "current_concepts": [ "Rate of Change Analysis", "Linear vs Nonlinear Functions" ] } ## Calculate rates of change for each table $$ \begin{aligned} &\text{Table 1: } \frac{1 - (-9)}{4 - 2} = \frac{10}{2} = 5, \quad \frac{11 - 1}{6 - 4} = \frac{10}{2} = 5 \quad (\text{Constant}) \ &\text{Table 2: } \frac{-16 - (-14)}{4 - 2} = \frac{-2}{2} = -1, \quad \frac{-18 - (-16)}{6 - 4} = \frac{-2}{2} = -1 \quad (\text{Constant}) \ &\text{Table 3: } \frac{6 - 0}{4 - 2} = \frac{6}{2} = 3, \quad \frac{16 - 6}{6 - 4} = \frac{10}{2} = 5 \quad (\text{Not constant}) \ &\text{Table 4: } \frac{-6 - (-9)}{4 - 2} = \frac{3}{2} = 1.5, \quad \frac{-3 - (-6)}{6 - 4} = \frac{3}{2} = 1.5 \quad (\text{Constant}) \end{aligned} $$ ## Identify the nonlinear function $$ \text{Table 3 has a non-constant rate of change, representing a nonlinear function.} $$

(A) Table 1: (2, -9), (4, 1), (6, 11)

(B) Table 2: (2, -14), (4, -16), (6, -18)

(C) Table 3: (2, 0), (4, 6), (6, 16)

(D) Table 4: (2, -9), (4, -6), (6, -3)

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Linear vs Nonlinear Functions" ] }

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Calculate rates of change for each table

Identify the nonlinear function

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