choose the function that represents the data in the table.

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
x & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
y & 5 & 14 & 29 & 50 & 77 & 110 \\
\hline
\end{tabular}

$y = 3x + 2$
$y = 3x^2 + 2$
$y = \frac{x}{3} + 2$
$y = 3^x + 2$

Question

choose the function that represents the data in the table.

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
x & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
y & 5 & 14 & 29 & 50 & 77 & 110 \\
\hline
\end{tabular}

$y = 3x + 2$
$y = 3x^2 + 2$
$y = \frac{x}{3} + 2$
$y = 3^x + 2$

Accepted Answer

{ "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", "Quadratic Modeling" ] } ## Evaluate the options at x = 1 $$ \begin{aligned} &\text{Option 1: } y = 3(1) + 2 = 5 \ &\text{Option 2: } y = 3(1)^2 + 2 = 5 \ &\text{Option 3: } y = \frac{1}{3} + 2 = 2.33 \ &\text{Option 4: } y = 3^1 + 2 = 5 \end{aligned} $$ ## Evaluate the remaining options at x = 2 $$ \begin{aligned} &\text{Option 1: } y = 3(2) + 2 = 8 eq 14 \ &\text{Option 2: } y = 3(2)^2 + 2 = 14 \ &\text{Option 4: } y = 3^2 + 2 = 11 eq 14 \end{aligned} $$ ## Verify the matching function at x = 3 $$ y = 3(3)^2 + 2 = 27 + 2 = 29 $$

$y = 3x + 2$

$y = 3x^2 + 2$

$y = \frac{x}{3} + 2$

$y = 3^x + 2$

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

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QUESTION IMAGE

Question

Explanation:

Evaluate the options at x = 1

Evaluate the remaining options at x = 2

Verify the matching function at x = 3

Answer: