Determine the Equation of the Horizontal Asymptote for the Graph $$f ( x ) = 4 ^ { x + 2 } - 2$$

question 35

Multiple Choice

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.
- $$f ( x ) = 4 ^ { x + 2 } - 2$$

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

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Definitions:

Long-Run Equilibrium

A state in which all factors of production and costs are variable, and firms in a competitive market have no incentive to enter or exit because they are earning normal profit.

Monopolistically Competitive Industry

An industry characterized by many firms offering products that are similar but not perfect substitutes, allowing for some degree of market power.

Monopolistic Competition

A market structure in which many companies sell products that are similar but not identical, allowing for competition among firms.

Demand Curve

A chart that illustrates the correlation between a product's price and the amount consumers want to buy.