the graph of $y = e^x$ is transformed as shown in the graph below. which equation represents the transformed function?

$y = e^{x-3}$
$y = e^x + 3$
$y = e^{x+3}$

Question

the graph of $y = e^x$ is transformed as shown in the graph below. which equation represents the transformed function?

$y = e^{x-3}$
$y = e^x + 3$
$y = e^{x+3}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Exponential Function Transformations", "Vertical Translation" ], "new_concepts": [], "current_concepts": [ "Exponential Function Transformations", "Vertical Translation", "Asymptotic Behavior of Logarithms" ] } ## Identify the parent function and its key features Using the *Exponential Function Transformations* knowledge point $$ \begin{aligned} &\text{Parent function: } y = e^x\ &\text{Horizontal asymptote of parent: } y = 0\ &\text{y-intercept of parent: } (0, 1) \end{aligned} $$ ## Analyze the transformed graph features Using the *Vertical Translation* knowledge point $$ \begin{aligned} &\text{Observed horizontal asymptote: } y = 3\ &\text{Observed y-intercept: } (0, 4) \end{aligned} $$ ## Determine the vertical shift Using the *Vertical Translation* knowledge point $$ \begin{aligned} &k = 3 - 0 = 3\ &y = e^x + 3 \end{aligned} $$

$y = e^{x-3}$

$y = e^x + 3$

$y = e^{x+3}$

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

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QUESTION IMAGE

Question

Explanation:

Identify the parent function and its key features

Analyze the transformed graph features

Determine the vertical shift

Answer: