which statement is true?

- the graph of $f$ is translated 3 units to the left and 4 units down.
- the graph of $f$ is translated 4 units to the left and 3 units up.
- the graph of $f$ is translated 4 units to the right and 3 units down.
- the graph of $f$ is translated 3 units to the right and 4 units up.

Question

which statement is true?

- the graph of $f$ is translated 3 units to the left and 4 units down.
- the graph of $f$ is translated 4 units to the left and 3 units up.
- the graph of $f$ is translated 4 units to the right and 3 units down.
- the graph of $f$ is translated 3 units to the right and 4 units up.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Function Transformations" ], "new_concepts": [], "current_concepts": [ "Function Transformations", "Square Root Functions" ] } ## Identify the parent function and the given function $$ \begin{aligned} &\text{Parent function: } f(x) = \sqrt{x}\ &\text{Transformed function: } g(x) = \sqrt{x + 3} - 4 \end{aligned} $$ ## Analyze the horizontal translation $$ \begin{aligned} &x \to x + 3 \implies \text{Shift left by 3 units} \end{aligned} $$ ## Analyze the vertical translation $$ \begin{aligned} &y \to y - 4 \implies \text{Shift down by 4 units} \end{aligned} $$

(A) The graph of $f$ is translated 3 units to the left and 4 units down.

(B) The graph of $f$ is translated 4 units to the left and 3 units up.

(C) The graph of $f$ is translated 4 units to the right and 3 units down.

(D) The graph of $f$ is translated 3 units to the right and 4 units up.

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

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QUESTION IMAGE

Question

Explanation:

Identify the parent function and the given function

Analyze the horizontal translation

Analyze the vertical translation

Answer: