Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.
-$$f ( x ) = 2 ^ { x + 3 }$$
A) Horizontal asymptote: $y = - 3$;
Domain: $( - \infty , \infty )$, Range: $( - 3 , \infty )$

B) Horizontal asymptote: $\mathrm { y } = 2$;
Domain: $( - \infty , \infty )$, Range: $( 2 , \infty )$

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

D) Horizontal asymptote: $\mathrm { y } = 3$;
Domain: $( - \infty , \infty )$, Range: $( 3 , \infty )$

Question

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.
-$$f ( x ) = 2 ^ { x + 3 }$$
A) Horizontal asymptote: $y = - 3$;
Domain: $( - \infty , \infty )$, Range: $( - 3 , \infty )$

B) Horizontal asymptote: $\mathrm { y } = 2$;
Domain: $( - \infty , \infty )$, Range: $( 2 , \infty )$

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

D) Horizontal asymptote: $\mathrm { y } = 3$;
Domain: $( - \infty , \infty )$, Range: $( 3 , \infty )$

Quizplus · Accepted Answer

The function $f(x) = 2^{x+3}$ is an exponential function, which has a horizontal asymptote at $y = 0$, because as $x$ approaches negative infinity, the function approaches 0 but never reaches it. The domain of any exponential function is all real numbers $(- \infty , \infty)$, and since the function is always positive, the range is $(0, \infty)$.

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

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