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: $( - 2 , \infty )$

Question

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: $( - 2 , \infty )$

Quizplus · Accepted Answer

The function $f(x) = 3^{x-2}$ approaches 0 as $x$ approaches negative infinity, making $y = 0$ the horizontal asymptote. The domain is all real numbers, and the range is all positive real numbers, including values greater than 0 but not 0 itself, hence $(0, \infty)$.

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

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