Question

Write the equation of the asymptote of the following function.f(x) = -4 (2)^x-3 + 5

Answer 1

Given: The equation below

`f(x)=-4(2)^(x-3)+5`

To Determine: The equation of the asymptote

Solution

Let us simplify the function

`\begin{gathered} f(x)=-4(2)^(x-3) \\ f(x)=-4*2^x/2^3+5 \\ f(x)=-4*2^x*(1)/(8)+5 \\ f(x)=-2^x/2+5 \\ f(x)=-2^(x-1)+5 \end{gathered}`

The graph is as shown below

From the above, the horizontal asymptote is y = 5