Solution:
Given:
[tex]y=e^{-x}-2[/tex]
The domain of a function is the set of input values that make the function defined.
Hence, for the function given, there are no undefined points for the function.
[tex]The\text{ domain is }-\infty
Thus, the domain in interval notation is:
[tex]\begin{gathered} \\ (-\infty,\infty) \end{gathered}[/tex]
The range of a function is the set of output values that make the function defined.
The range of the exponential function is given by:
[tex]y>-2[/tex]
Therefore, in interval notation, the range is:
[tex](-2,\infty)[/tex]
The asymptote is a line that a graph approaches without touching it.
The graph of the function is shown:
Hence, it has a horizontal asymptote as the curve bends towards the horizontal line at y = -2.
Therefore, the asymptote exists at y = -2
