which of the following is the graph of this square root function?

\f(x) = \sqrt{x - 2} + 3\

Question

which of the following is the graph of this square root function?

\f(x) = \sqrt{x - 2} + 3\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Graphing Radical Functions", "Radical Function Transformations", "Square Root Graphs" ], "new_concepts": [], "current_concepts": [ "Graphing Radical Functions", "Radical Function Transformations", "Square Root Graphs" ] } ## Identify the starting point of the function Using the *Graphing Radical Functions* and *Radical Function Transformations* knowledge points $$ \begin{aligned} &f(x) = \sqrt{x - 2} + 3\ &\text{Domain restriction: } x - 2 \ge 0 \implies x \ge 2\ &\text{Starting point } (h, k) = (2, 3) \end{aligned} $$ ## Evaluate an additional point on the curve Using the *Square Root Graphs* knowledge point $$ \begin{aligned} &x = 6 \implies f(6) = \sqrt{6 - 2} + 3 = \sqrt{4} + 3 = 5\ &\text{Point on graph: } (6, 5) \end{aligned} $$ ## Match with the correct graph option Using the *Square Root Graphs* knowledge point $$ \begin{aligned} &\text{Graph 1 starting point: } (2, 1) \quad \text{(Incorrect)}\ &\text{Graph 2 starting point: } (2, 3) \quad \text{(Correct)}\ &\text{Graph 3 starting point: } (-3, 3) \quad \text{(Incorrect)} \end{aligned} $$

(A) Graph with starting point at (2, 1)

(B) Graph with starting point at (2, 3)

(C) Graph with starting point at (-3, 3)

{ "elements": [ { "type": "point", "params": [[2, 3]], "properties": { "name": "Starting Point (2,3)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[6, 5]], "properties": { "name": "(6,5)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "Math.sqrt(x - 2) + 3", "latex": "\sqrt{x - 2} + 3"}, 2, 10], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3 } } ], "timestamps": [0.5, 1.0, 1.5] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Square Root Graphs" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the starting point of the function

Evaluate an additional point on the curve

Match with the correct graph option

Answer: