which of the following is the graph of this square root function?
\f(x) = \sqrt{x - 2} + 2\

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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": [ "Domain of Radical Functions", "Radical Function Transformations", "Square Root Graphs" ], "new_concepts": [], "current_concepts": [ "Domain of Radical Functions", "Radical Function Transformations", "Square Root Graphs" ] } ## Find the domain of the function Using the *Domain of Radical Functions* knowledge point $$ \begin{aligned} x - 2 &\ge 0 \ x &\ge 2 \end{aligned} $$ ## Identify the starting point Using the *Radical Function Transformations* and *Square Root Graphs* knowledge points $$ \begin{aligned} f(2) &= \sqrt{2 - 2} + 2 \ &= 0 + 2 \ &= 2 \end{aligned} $$ The starting point of the graph is $(2, 2)$. ## Evaluate an additional point Using the *Square Root Graphs* knowledge point $$ \begin{aligned} f(6) &= \sqrt{6 - 2} + 2 \ &= \sqrt{4} + 2 \ &= 2 + 2 \ &= 4 \end{aligned} $$ The graph passes through the point $(6, 4)$. ## Match with the given graphs Analyzing the three options: - First graph: Starts at $(-2, -2)$. - Second graph: Starts at $(-1, 2)$. - Third graph: Starts at $(2, 2)$ and passes through $(6, 4)$.

(A) Graph starting at $(-2, -2)$

(B) Graph starting at $(-1, 2)$

(C) Graph starting at $(2, 2)$

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Question

Explanation:

Find the domain of the function

Identify the starting point

Evaluate an additional point

Match with the given graphs

Answer: