select the correct answer.

consider function f.

\f(x) = \sqrt{x - 1}\

which graph represents function f?

Question

select the correct answer.

consider function f.

\f(x) = \sqrt{x - 1}\

which graph represents function f?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Radical Function Graphs", "Domain of a Function" ], "new_concepts": [], "current_concepts": [ "Radical Function Graphs", "Domain of a Function", "Function Transformations" ] } ## Determine the domain and starting point of the function $$ \begin{aligned} x - 1 &\ge 0 \ x &\ge 1 \ \text{Starting point: } &(1, 0) \end{aligned} $$ ## Evaluate key points on the graph $$ \begin{aligned} f(1) &= \sqrt{1 - 1} = 0 \ f(2) &= \sqrt{2 - 1} = 1 \ f(5) &= \sqrt{5 - 1} = 2 \end{aligned} $$ ## Match points to the given graphs $$ \begin{aligned} \text{Graph W: } &\text{Starts at } (-1, 0) \text{ and goes left} \ \text{Graph X: } &\text{Starts at } (-1, 0) \text{ and goes right} \ \text{Graph Y: } &\text{Starts at } (1, 0) \text{ and goes right, passing through } (2, 1) \text{ and } (5, 2) \ \text{Graph Z: } &\text{Starts at } (1, 0) \text{ and goes left} \end{aligned} $$

W.

X.

Y.

Z.

{ "elements": [ { "type": "functiongraph", "params": [ { "js": "Math.sqrt(x - 1)", "latex": "\sqrt{x - 1}" }, 1, 10 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3, "name": "f(x) = \sqrt{x-1}", "withLabel": true } }, { "type": "point", "params": [[1, 0]], "properties": { "name": "(1,0)", "size": 4, "color": "#F2557F", "strokeColor": "#F2557F", "withLabel": true } }, { "type": "point", "params": [[2, 1]], "properties": { "name": "(2,1)", "size": 4, "color": "#F2557F", "strokeColor": "#F2557F", "withLabel": true } }, { "type": "point", "params": [[5, 2]], "properties": { "name": "(5,2)", "size": 4, "color": "#F2557F", "strokeColor": "#F2557F", "withLabel": true } } ], "timestamps": [0.5, 1.0, 1.5] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Radical Function Graphs" ] }

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QUESTION IMAGE

Question

Explanation:

Determine the domain and starting point of the function

Evaluate key points on the graph

Match points to the given graphs

Answer: