Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.
-$$f ( x ) = e ^ { 3 x } - 4$$
A) Horizontal asymptote: $\mathrm { y } = 0$;
Domain: $( - \infty , \infty )$, Range: $( 0 , \infty )$

B) Horizontal asymptote: $\mathrm { y } = - 4$;
Domain: $( - \infty , \infty )$, Range: $( - 4 , \infty )$

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

D) Horizontal asymptote: $\mathrm { y } = 4$;
Domain: $( - \infty , \infty )$, Range: $( 4 , \infty )$

Question

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.
-$$f ( x ) = e ^ { 3 x } - 4$$
A) Horizontal asymptote: $\mathrm { y } = 0$;
Domain: $( - \infty , \infty )$, Range: $( 0 , \infty )$

B) Horizontal asymptote: $\mathrm { y } = - 4$;
Domain: $( - \infty , \infty )$, Range: $( - 4 , \infty )$

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

D) Horizontal asymptote: $\mathrm { y } = 4$;
Domain: $( - \infty , \infty )$, Range: $( 4 , \infty )$

Quizplus · Accepted Answer

The horizontal asymptote of $f(x) = e^{3x} - 4$ is $y = -4$, because as $x$ approaches $-\infty$, $e^{3x}$ approaches 0, leaving $y = -4$. The domain of any exponential function is all real numbers, $(- \infty , \infty )$, and since the function can take any value greater than $-4$, the range is $(-4, \infty)$.

Determine the Equation of the Horizontal Asymptote for the Graph f(x)=e3x−4f ( x ) = e ^ { 3 x } - 4f(x)=e3x−4

Determine the Equation of the Horizontal Asymptote for the Graph $f ( x ) = e ^ { 3 x } - 4$