which inequality represents the domain of the exponential piece?

$x \le -2$

$x 3$

$x 1$

$x \ge -1$

Question

which inequality represents the domain of the exponential piece?

$x \le -2$

$x > 3$

$x > 1$

$x \ge -1$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Piecewise Functions", "Domain of a Function" ], "new_concepts": [], "current_concepts": [ "Piecewise Functions", "Domain of a Function", "Exponential Functions" ] } ## Identify the pieces of the function $$ \begin{aligned} &\text{Left piece: Quadratic curve defined for } x \le -2\ &\text{Right piece: Exponential curve starting at } x = -2 \text{ and increasing rapidly} \end{aligned} $$ ## Determine the boundary of the exponential piece $$ \begin{aligned} &\text{The transition point between the two curves occurs at } x = -2\ &\text{The exponential curve is defined for all values of } x \text{ to the right of and including } -2 \end{aligned} $$ ## Match with the given options $$ \begin{aligned} &\text{Domain of the exponential piece: } x \ge -2 \end{aligned} $$

(A) $x \ge -2$

(B) $x > 3$

(C) $x > 1$

(D) $x \ge -1$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Piecewise Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the pieces of the function

Determine the boundary of the exponential piece

Match with the given options

Answer: