Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function.
-$f(x)=5^{x-2}-1$
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: $\mathrm{y}=1$;
Domain: $(-\infty, \infty)$, Range: $(1, \infty)$
D) Horizontal asymptote: $\mathrm{y}=-1$;
Domain: $(-\infty, \infty)$, Range: $(-1, \infty)$

Question

Quizplus · Accepted Answer

The horizontal asymptote of $f(x) = 5^{x-2} - 1$ is $y = -1$, because as $x$ approaches $\pm\infty$, $5^{x-2}$ approaches $+\infty$ or $0$, and subtracting $1$ shifts the asymptote to $y = -1$. The domain of any exponential function is all real numbers, $(-\infty, \infty)$, and since the function can take any value greater than $-1$, the range is $(-1, \infty)$.

Determine the Equation of the Horizontal Asymptote for the Graph f(x)=5x−2−1f(x)=5^{x-2}-1f(x)=5x−2−1

Determine the Equation of the Horizontal Asymptote for the Graph $f(x)=5^{x-2}-1$