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

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: $( 0 , \infty )$