choose the function that represents the data in the table.

\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & 0 & 1 & 2 & 3 & 4 & 5 \\
\hline
y & -3 & -1 & 5 & 15 & 29 & 47 \\
\hline
\end{array}

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

$y = 2^x - 3$

$y = 2x - 3$

$y = 2x^2 - 3$

Question

choose the function that represents the data in the table.

\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & 0 & 1 & 2 & 3 & 4 & 5 \\
\hline
y & -3 & -1 & 5 & 15 & 29 & 47 \\
\hline
\end{array}

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

$y = 2^x - 3$

$y = 2x - 3$

$y = 2x^2 - 3$

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", "Second Differences", "Quadratic Modeling" ], "new_concepts": [], "current_concepts": [ "Function Evaluation", "Second Differences", "Quadratic Modeling" ] } ## Analyze the initial value $$ \text{At } x = 0, \quad y = -3 $$ ## Test the given options at key points $$ \begin{aligned} &\text{For } y = \frac{x}{2} - 3: \quad x = 1 \implies y = -2.5 eq -1 \ &\text{For } y = 2^x - 3: \quad x = 1 \implies y = 2^1 - 3 = -1, \quad x = 2 \implies y = 2^2 - 3 = 1 eq 5 \ &\text{For } y = 2x - 3: \quad x = 1 \implies y = 2(1) - 3 = -1, \quad x = 2 \implies y = 2(2) - 3 = 1 eq 5 \ &\text{For } y = 2x^2 - 3: \quad x = 1 \implies y = 2(1)^2 - 3 = -1, \quad x = 2 \implies y = 2(2)^2 - 3 = 5 \end{aligned} $$ ## Verify the quadratic model for remaining points $$ \begin{aligned} &x = 3 \implies y = 2(3)^2 - 3 = 15 \ &x = 4 \implies y = 2(4)^2 - 3 = 29 \ &x = 5 \implies y = 2(5)^2 - 3 = 47 \end{aligned} $$

(A) $y = \frac{x}{2} - 3$

(B) $y = 2^x - 3$

(C) $y = 2x - 3$

(D) $y = 2x^2 - 3$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Modeling" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Analyze the initial value

Test the given options at key points

Verify the quadratic model for remaining points

Answer: