identify the horizontal asymptote of each graph.

graph 1:
$f(x) = 6^x$
options:
- $y = 0$
- $y = 1$
- $y = 6$

graph 2:
$f(x) = 5^x - 3$
options:
- $y = 0$
- $y = -3$
- $y = -5$

Question

identify the horizontal asymptote of each graph.

graph 1:
$f(x) = 6^x$
options:
- $y = 0$
- $y = 1$
- $y = 6$

graph 2:
$f(x) = 5^x - 3$
options:
- $y = 0$
- $y = -3$
- $y = -5$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Exponential Function Graphs", "Exponential Function Transformations" ], "new_concepts": [], "current_concepts": [ "Exponential Function Graphs", "Exponential Function Transformations", "Horizontal Asymptotes" ] } ## Analyze the first graph Using the *Exponential Function Graphs* knowledge point $$ \begin{aligned} &f(x) = 6^x\ &\lim_{x \to -\infty} 6^x = 0\ &\text{Horizontal asymptote: } y = 0 \end{aligned} $$ ## Analyze the second graph Using the *Exponential Function Transformations* knowledge point $$ \begin{aligned} &f(x) = 5^x - 3\ &\lim_{x \to -\infty} (5^x - 3) = 0 - 3 = -3\ &\text{Horizontal asymptote: } y = -3 \end{aligned} $$ ## Question 1 (A) $y = 0$

(B) $y = 1$

(C) $y = 6$ ## Question 2 (A) $y = 0$

(B) $y = -3$

(C) $y = -5$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Analyze the first graph

Analyze the second graph

Answer:

Question 1

Question 2