The function given is $h(x) = -e - 10$.

Since this function is constant (it doesn't depend on $x$), it represents a horizontal line at $y = -e - 10$.

Horizontal Asymptote:

A horizontal asymptote occurs when the value of the function approaches a constant value as $x$ approaches $\pm \infty$. In this case, the function is already constant, so the horizontal asymptote is simply the value of the function itself.

Thus, the horizontal asymptote is: $y = -e - 10$

Since $e \approx 2.718$, the approximate numerical value is: $y \approx -2.718 - 10 = -12.718$

Tip:

A constant function like this will always have the same value across its domain, so the graph is a straight line, and the horizontal asymptote is just the line itself.

Would you like more details on how to graph such functions or any other questions?

Follow-up questions:

1. What is the general definition of a horizontal asymptote?
2. How do horizontal asymptotes behave in exponential functions?
3. Can there be a vertical asymptote for a constant function?
4. How does the value of $e$ impact other functions, such as $e^x$?
5. How would the horizontal asymptote change if we added an $x$-term to the equation?