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

B) Horizontal asymptote: $\mathbf { y } = - 1$;
Domain: $( - \infty , \infty )$, Range: $( - 1 , \infty )$

C) Horizontal asymptote: $\mathrm { y } = 1$;
Domain: $( - \infty , \infty )$, Range: $( 1 , \infty )$

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

Question

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

B) Horizontal asymptote: $\mathbf { y } = - 1$;
Domain: $( - \infty , \infty )$, Range: $( - 1 , \infty )$

C) Horizontal asymptote: $\mathrm { y } = 1$;
Domain: $( - \infty , \infty )$, Range: $( 1 , \infty )$

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

Quizplus · Accepted Answer

The horizontal asymptote is found by evaluating the limit of $f(x)$ as $x$ approaches negative infinity. For $f(x) = e^{x-1} + 1$, as $x$ approaches negative infinity, $e^{x-1}$ approaches 0, making the horizontal asymptote $y = 1$. The domain of any exponential function is all real numbers, $(- \infty , \infty )$, and since $e^{x-1}$ is always positive and we add 1 to it, the range is $(1, \infty)$.

Determine the Equation of the Horizontal Asymptote for the Graph f(x)=ex−1+1f ( x ) = e ^ { x - 1 } + 1f(x)=ex−1+1

Determine the Equation of the Horizontal Asymptote for the Graph $f ( x ) = e ^ { x - 1 } + 1$