which statement best describes the domain and range of (p(x) = 6^{-x}) and (q(x) = 6^x)?

- (p(x)) and (q(x)) have different domains but the same range.
- (p(x)) and (q(x)) have different domains and different ranges.
- (p(x)) and (q(x)) have the same domain and the same range.
- (p(x)) and (q(x)) have the same domain but different ranges.

Question

which statement best describes the domain and range of (p(x) = 6^{-x}) and (q(x) = 6^x)?

- (p(x)) and (q(x)) have different domains but the same range.
- (p(x)) and (q(x)) have different domains and different ranges.
- (p(x)) and (q(x)) have the same domain and the same range.
- (p(x)) and (q(x)) have the same domain but different ranges.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponential Domain", "Exponential Range" ], "new_concepts": [], "current_concepts": [ "Exponential Domain", "Exponential Range" ] } ## Analyze the domains of the functions $$ \begin{aligned} &\text{Domain of } p(x) = 6^{-x}: \quad (-\infty, \infty) \ &\text{Domain of } q(x) = 6^x: \quad (-\infty, \infty) \end{aligned} $$ ## Analyze the ranges of the functions $$ \begin{aligned} &\text{Range of } p(x) = 6^{-x}: \quad (0, \infty) \ &\text{Range of } q(x) = 6^x: \quad (0, \infty) \end{aligned} $$ ## Compare domains and ranges $$ \begin{aligned} &\text{Domain}(p) = \text{Domain}(q) \ &\text{Range}(p) = \text{Range}(q) \end{aligned} $$

$p(x)$ and $q(x)$ have different domains but the same range.

$p(x)$ and $q(x)$ have different domains and different ranges.

$p(x)$ and $q(x)$ have the same domain and the same range.

$p(x)$ and $q(x)$ have the same domain but different ranges.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Domain" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the domains of the functions

Analyze the ranges of the functions

Compare domains and ranges

Answer: