thomas is building rectangular boxes. the table shows the area in square feet, (f(x)), of the bottom of a box when one side of the box is (x) feet long.

choose the function that represents the data.

- (f(x) = x^2 + 2x)
- (f(x) = \frac{x^2}{2})
- (f(x) = 2x^2)
- (f(x) = 2x)

Question

thomas is building rectangular boxes. the table shows the area in square feet, (f(x)), of the bottom of a box when one side of the box is (x) feet long.

choose the function that represents the data.

- (f(x) = x^2 + 2x)
- (f(x) = \frac{x^2}{2})
- (f(x) = 2x^2)
- (f(x) = 2x)

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", "Quadratic Modeling" ], "new_concepts": [], "current_concepts": [ "Function Evaluation", "Quadratic Modeling" ] } ## Evaluate the options at x = 1 $$ \begin{aligned} &f(1) = 1^2 + 2(1) = 3 eq 2\ &f(1) = \frac{1^2}{2} = 0.5 eq 2\ &f(1) = 2(1^2) = 2\ &f(1) = 2(1) = 2 \end{aligned} $$ ## Evaluate the remaining options at x = 2 $$ \begin{aligned} &f(2) = 2(2^2) = 2(4) = 8\ &f(2) = 2(2) = 4 eq 8 \end{aligned} $$ ## Verify the matching function for all data points $$ \begin{aligned} &f(3) = 2(3^2) = 2(9) = 18\ &f(4) = 2(4^2) = 2(16) = 32\ &f(5) = 2(5^2) = 2(25) = 50 \end{aligned} $$

(A) $f(x) = x^2 + 2x$

(B) $f(x) = \frac{x^2}{2}$

(C) $f(x) = 2x^2$

(D) $f(x) = 2x$

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

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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 for all data points

Answer: