question 9

what is the asymptote for the function (f(x) = -3^x - 4)?

$y = 4$
$x = -4$
$y = -4$

Question

question 9

what is the asymptote for the function (f(x) = -3^x - 4)?

$y = 4$
$x = -4$
$y = -4$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Exponential Asymptotes" ], "new_concepts": [], "current_concepts": [ "Exponential Asymptotes", "Asymptotes of Functions" ] } ## Identify the function type Using the *Exponential Asymptotes* knowledge point $$ f(x) = -3^x - 4 $$ ## Determine the horizontal asymptote Using the *Exponential Asymptotes* knowledge point $$ \begin{aligned} &\lim_{x \to -\infty} 3^x = 0\ &\lim_{x \to -\infty} (-3^x - 4) = 0 - 4 = -4\ &\text{Horizontal Asymptote: } y = -4 \end{aligned} $$

$y = 4$

$x = -4$

$y = -4$

{ "elements": [ { "type": "line", "params": [[-10, -4], [10, -4]], "properties": { "name": "y = -4", "strokeColor": "#F2557F", "strokeWidth": 2, "dash": 2, "withLabel": true, "labelPosition": [8, -3.5] } }, { "type": "functiongraph", "params": [{"js": "-Math.pow(3, x) - 4", "latex": "f(x) = -3^x - 4"}, -10, 1.5], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3 } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Asymptotes" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the function type

Determine the horizontal asymptote

Answer: