\f(x) = \sqrt3{x - 2}\

which graph represents function $f$?

Question

\f(x) = \sqrt3{x - 2}\

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", "Graph Intercepts" ], "new_concepts": [], "current_concepts": [ "Radical Function Graphs", "Graph Intercepts", "Cube Root Functions" ] } ## Determine the key features of the function $$ f(x) = \sqrt[3]{x - 2} $$ $$ \begin{aligned} &\text{Domain: } x \in \mathbb{R}\ &\text{Inflection point (center of symmetry): } (2, 0)\ &\text{y-intercept: } f(0) = \sqrt[3]{-2} \approx -1.26 \end{aligned} $$ ## Analyze the behavior of the function $$ \begin{aligned} &\text{For } x > 2: f(x) > 0 \text{ and increasing}\ &\text{For } x < 2: f(x) < 0 \text{ and increasing} \end{aligned} $$ ## Match with the given graphs $$ \begin{aligned} &\text{Graph W: Center at } (2, 0), \text{ decreasing (incorrect)}\ &\text{Graph X: Center at } (-2, 0) \text{ (incorrect)}\ &\text{Graph Y: Center at } (2, 0), \text{ increasing (correct)}\ &\text{Graph Z: Center at } (-2, 0) \text{ (incorrect)} \end{aligned} $$

W.

X.

Y.

Z.

{ "elements": [ { "type": "functiongraph", "params": [ { "js": "Math.cbrt(x - 2)", "latex": "\sqrt[3]{x - 2}" }, -8, 8 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2.5, "name": "f(x)", "withLabel": true } }, { "type": "point", "params": [[2, 0]], "properties": { "name": "(2,0)", "size": 4, "color": "#F2557F", "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Radical Function Graphs" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Determine the key features of the function

Analyze the behavior of the function

Match with the given graphs

Answer: