Respuesta :
Explanation
The asymptote of the graph
[tex]f\mleft(x\mright)=5^x-1[/tex]can be seen below.
Horizontal Asymptote
Line y=L is a horizontal asymptote of the function y=f(x), if either
[tex]lim_{x→∞}f\mleft(x\mright)=L\text{ }or\text{ }lim_{x→−∞}f\mleft(x\mright)=L,and\text{ }L\text{ }is\text{ }finite.[/tex]Therefore,
[tex]\begin{gathered} \lim_{x\to+\infty\:}\left(5^x-1\right)=\infty \\ \lim_{x\to-\infty\:}\left(5^x-1\right)=-1 \end{gathered}[/tex]Answer: Thus, the horizontal asymptote is y = −1.
Vertical Asymptote
The line x=L is a vertical asymptote of the function y=5^x−1, if the limit of the function (one-sided) at this point is infinite.
In other words, it means that possible points are points where the denominator equals 0 or doesn't exist.
So, find the points where the denominator equals 0 and check them.
As can be seen, there are no such points, so this function doesn't have vertical asymptotes
Answer: No vertical asymptote
