Solution:
Given the function:
![f(x)=-3\log_2(x_+4)-5](https://img.qammunity.org/2023/formulas/mathematics/college/pv1tl2x4t1z8ki57di9hh1votr2155fo5j.png)
To determine the equation of the asymptote, we first plot the graph of the function.
Thus, for various values of x and y, the graph of the function is shown below:
The asymptote is a line such that the distance between the graphed curve and the line approaches zero when the x or y coordinate approaches infinity.
In the above curve, the asymptote is at
![x=-4](https://img.qammunity.org/2023/formulas/mathematics/high-school/wcn1xvhdqswk4z8d45ock4ayhxlpyrm9zt.png)
Hence, the equation of the asymptote is expressed as
![x=-4](https://img.qammunity.org/2023/formulas/mathematics/high-school/wcn1xvhdqswk4z8d45ock4ayhxlpyrm9zt.png)