Determine the Equation of the Horizontal Asymptote for the Graph $$f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x } - 2$$

question 24

Essay

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.
- $$f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x } - 2$$
A) Horizontal asymptote: $y = - 2$ ;
Domain: $( - \infty , \infty )$ , Range: $( - 2 , \infty )$

B) Horizontal asymptote: $\mathrm { y } = \frac { 1 } { 5 }$ ;
Domain: $( - \infty , \infty )$ , Range: $\left( \frac { 1 } { 5 } , \infty \right)$

C) Horizontal asymptote: $y = 2$ ;
Domain: $( - \infty , \infty )$ , Range: $( 2 , \infty )$

D) Horizontal asymptote: $\mathrm { y } = 0$ ;
Domain: $( - \infty , \infty )$ , Range: $( 0 , \infty )$

• A) Horizontal asymptote: \(y = - 2\);
• Domain: \(( - \infty , \infty )\), Range: \(( - 2 , \infty )\)
• B) Horizontal asymptote: \(\mathrm { y } = \frac { 1 } { 5 }\);
• Domain: \(( - \infty , \infty )\), Range: \(\left( \frac { 1 } { 5 } , \infty \right)\)
• C) Horizontal asymptote: \(y = 2\);
• Domain: \(( - \infty , \infty )\), Range: \(( 2 , \infty )\)
• D) Horizontal asymptote: \(\mathrm { y } = 0\);
• Domain: \(( - \infty , \infty )\), Range: \(( 0 , \infty )\)

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Definitions:

Labor Taxes

Financial obligations placed on workers or their employers, calculated as a portion of the salaries paid to employees.

Consumer Surplus

The differentiation between the amount consumers are ready to disburse for a product or service and the amount they actually disburse.

Producer Surplus

The difference between the amount that a producer is actually paid for a good compared to the minimum amount they would be willing to accept for the good.

Elasticity of Demand

A measure of how much the demand for a product changes in response to a change in the price of that product.