consider the functions f and g as shown in the graph to the right.

graph g - f.

choose the correct graph below.

Question

consider the functions f and g as shown in the graph to the right.

graph g - f.

choose the correct graph below.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Graphical Function Evaluation" ], "new_concepts": [ "Function Subtraction Graphically" ], "current_concepts": [ "Graphical Function Evaluation", "Function Subtraction Graphically" ] } ## Identify key points of functions F and G $$ \begin{aligned} &\text{Domain of } G: [2, 11]\ &\text{Domain of } F: [3, 12]\ &\text{Common Domain for } G - F: [3, 11]\ &x = 3: G(3) = 3,\ F(3) = -2 \implies (G-F)(3) = 3 - (-2) = 5\ &x = 4: G(4) = 6,\ F(4) = 0 \implies (G-F)(4) = 6 - 0 = 6\ &x = 7: G(7) = 5,\ F(7) = 8 \implies (G-F)(7) = 5 - 8 = -3\ &x = 11: G(11) = 1,\ F(11) = 3 \implies (G-F)(11) = 1 - 3 = -2 \end{aligned} $$ ## Match calculated values with the options $$ \begin{aligned} &\text{Key coordinates for } G - F: (3, 5), (4, 6), (7, -3), (11, -2)\ &\text{Option A has points: } (3, 5), (4, 6), (7, -3), (11, -2)\ &\text{Option B has points: } (3, -5), (4, -6), (7, 3), (11, 2) \quad (\text{this is } F - G)\ &\text{Option C has points: } (3, 6), (4, 7), (7, -2), (11, -1)\ &\text{Option D has points: } (3, -5), (4, -4), (7, 3), (11, 2) \end{aligned} $$

(A) Graph starting at (3, 5), rising to (4, 6), dropping to (7, -3), and ending at (11, -2)

(B) Graph starting at (3, -5), dropping to (4, -6), rising to (7, 3), and ending at (11, 2)

(C) Graph starting at (3, 6), rising to (4, 7), dropping to (7, -2), and ending at (11, -1)

(D) Graph starting at (3, -5), rising to (4, -4), rising to (7, 3), and ending at (11, 2)

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

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QUESTION IMAGE

Question

Explanation:

Identify key points of functions F and G

Match calculated values with the options

Answer: