which statement best describes the domain and range of $f(x) = -(7)^x$ and $g(x) = 7^x$?

$f(x)$ and $g(x)$ have the same domain and the same range.
$f(x)$ and $g(x)$ have the same domain but different ranges.
$f(x)$ and $g(x)$ have different domains but the same range.
$f(x)$ and $g(x)$ have different domains and different ranges.

Question

which statement best describes the domain and range of $f(x) = -(7)^x$ and $g(x) = 7^x$?

$f(x)$ and $g(x)$ have the same domain and the same range.
$f(x)$ and $g(x)$ have the same domain but different ranges.
$f(x)$ and $g(x)$ have different domains but the same range.
$f(x)$ and $g(x)$ have different domains and 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 Transformations", "Asymptotic Behavior" ], "new_concepts": [], "current_concepts": [ "Exponential Transformations", "Asymptotic Behavior", "Domain and Range" ] } ## Analyze the domains of both functions $$ \begin{aligned} &\text{Domain of } g(x) = 7^x: \quad (-\infty, \infty)\ &\text{Domain of } f(x) = -(7)^x: \quad (-\infty, \infty) \end{aligned} $$ ## Analyze the ranges of both functions $$ \begin{aligned} &\text{Range of } g(x) = 7^x: \quad (0, \infty)\ &\text{Range of } f(x) = -(7)^x: \quad (-\infty, 0) \end{aligned} $$ ## Compare domains and ranges $$ \begin{aligned} &\text{Domains: } \text{Same} \quad ((-\infty, \infty))\ &\text{Ranges: } \text{Different} \quad ((-\infty, 0) eq (0, \infty)) \end{aligned} $$

$f(x)$ and $g(x)$ have the same domain and the same range.

$f(x)$ and $g(x)$ have the same domain but different ranges.

$f(x)$ and $g(x)$ have different domains but the same range.

$f(x)$ and $g(x)$ have different domains and different ranges.

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

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QUESTION IMAGE

Question

Explanation:

Analyze the domains of both functions

Analyze the ranges of both functions

Compare domains and ranges

Answer: