the graph of (g) is a translation 3 units down of the graph of (f(x) = x^2 + 2). what is the range of (g)?

a. (g(x) \ge -3)
b. (g(x) \ge -1)
c. (g(x) \ge 1)
d. all real numbers

Question

the graph of (g) is a translation 3 units down of the graph of (f(x) = x^2 + 2). what is the range of (g)?

a. (g(x) \ge -3)
b. (g(x) \ge -1)
c. (g(x) \ge 1)
d. all real numbers

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", "Quadratic Range" ], "new_concepts": [], "current_concepts": [ "Function Transformations", "Quadratic Range", "Graphing Quadratic Functions" ] } ## Determine the equation of the translated function $$ \begin{aligned} f(x) &= x^2 + 2 \ g(x) &= f(x) - 3 \ g(x) &= (x^2 + 2) - 3 \ g(x) &= x^2 - 1 \end{aligned} $$ ## Find the range of the quadratic function $$ \begin{aligned} x^2 &\ge 0 \quad \text{for all real } x \ x^2 - 1 &\ge -1 \ g(x) &\ge -1 \end{aligned} $$

A. $g(x) \ge -3$

B. $g(x) \ge -1$

C. $g(x) \ge 1$

D. all real numbers

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Range" ] }

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Question

Explanation:

Determine the equation of the translated function

Find the range of the quadratic function

Answer: