how does the graph of $n(x) = m(x) + 12$ compare to the graph of $m(x) = x^2 - 22$?

- the function $m(x)$ is translated 12 units to the left to form $n(x)$.
- the function $m(x)$ is translated 10 units to the left to form $n(x)$.
- the function $m(x)$ is translated 12 units upward to form $n(x)$.
- the function $m(x)$ is translated 10 units upward to form $n(x)$.

Question

how does the graph of $n(x) = m(x) + 12$ compare to the graph of $m(x) = x^2 - 22$?

- the function $m(x)$ is translated 12 units to the left to form $n(x)$.
- the function $m(x)$ is translated 10 units to the left to form $n(x)$.
- the function $m(x)$ is translated 12 units upward to form $n(x)$.
- the function $m(x)$ is translated 10 units upward to form $n(x)$.

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", "Quadratic Functions" ] } ## Identify the transformation rule $$ n(x) = m(x) + c $$ ## Apply the vertical translation $$ \begin{aligned} &c = 12 > 0\ &\text{Translation: } 12 \text{ units upward} \end{aligned} $$ ## Match with the options $$ \text{The function } m(x) \text{ is translated } 12 \text{ units upward to form } n(x). $$

The function $m(x)$ is translated 12 units to the left to form $n(x)$.

The function $m(x)$ is translated 10 units to the left to form $n(x)$.

The function $m(x)$ is translated 12 units upward to form $n(x)$.

The function $m(x)$ is translated 10 units upward to form $n(x)$.

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

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QUESTION IMAGE

Question

Explanation:

Identify the transformation rule

Apply the vertical translation

Match with the options

Answer: