Given: The equation below
[tex]f(x)=-4(2)^{x-3}+5[/tex]
To Determine: The equation of the asymptote
Solution
Let us simplify the function
[tex]\begin{gathered} f(x)=-4(2)^{x-3} \\ f(x)=-4\times2^x\div2^3+5 \\ f(x)=-4\times2^x\times\frac{1}{8}+5 \\ f(x)=-2^x\div2+5 \\ f(x)=-2^{x-1}+5 \end{gathered}[/tex]
The graph is as shown below
From the above, the horizontal asymptote is y = 5
