The equation of the asymptote is [tex]y=1[/tex]
Explanation:
The given equation is [tex]f(x)=3^{x-5}+1[/tex]
We need to determine the horizontal asymptote of the equation.
The given equation is of the exponential function of the form [tex]f(x)=c \cdot n^{a x+b}+k[/tex] and has a horizontal asymptote [tex]y=k[/tex]
Hence, from the above equation, the value of k is 1.
Therefore, we have,
[tex]k=1[/tex]
Thus, the horizontal asymptote is [tex]y=1[/tex]
Therefore, the asymptote of the equation is [tex]y=1[/tex]
