Determine the Equation of the Horizontal Asymptote for the Graph $$f ( x ) = 3 ^ { x - 2 }$$

question 116

Multiple Choice

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.
- $$f ( x ) = 3 ^ { x - 2 }$$

• A) Horizontal asymptote: \(y = 3\);
• Domain: \(( - \infty , \infty )\), Range: \(( 3 , \infty )\)
• B) Horizontal asymptote: \(\mathrm { y } = 0\);
• Domain: \(( - \infty , \infty )\), Range: \(( 0 , \infty )\)
• C) Horizontal asymptote: \(y = 2\);
• Domain: \(( - \infty , \infty )\), Range: \(( 2 , \infty )\)
• D) Horizontal asymptote: \(y = - 2\);
• Domain: \(( - \infty , \infty )\), Range: \(( - 2 , \infty )\)

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Definitions:

Magical Thinking

Magical thinking is the belief that one's thoughts, words, or actions can bring about something in the external world simply by personal will, bypassing the laws of physics and causation.

Self-Concept

Self-concept is the understanding or perception that one has of oneself, including beliefs about one's attributes, like skills, abilities, and appearance.

Global Empathy

The capacity to understand and share the feelings of people from diverse cultures and backgrounds across the world.

Egocentric Empathy

The limited ability to understand another's perspective, assuming others feel the same as oneself.