Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of thisfunction.
-$f(x)=3^{x-2}$
A) Horizontal asymptote: $\mathrm{y}=-2$;
Domain: $(-\infty, \infty)$, Range: $(-2, \infty)$
B) Horizontal asymptote: $\mathrm{y}=0$;
Domain: $(-\infty, \infty)$, Range: $(0, \infty)$
C) Horizontal asymptote: $\mathrm{y}=2$;
Domain: $(-\infty, \infty)$, Range: $(2, \infty)$
D) Horizontal asymptote: $\mathrm{y}=3$;
Domain: $(-\infty, \infty)$, Range: $(3, \infty)$

Question

Quizplus · Accepted Answer

The function $f(x)=3^{x-2}$ is an exponential function, which always has a horizontal asymptote at $y=0$, regardless of the horizontal shift. The domain of any exponential function is all real numbers $(-\infty, \infty)$, and since exponential functions are always positive, the range is $(0, \infty)$.

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 $f(x)=3^{x-2}$