State the horizontal asymptote for the function h (x) = -e − 10:

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?



State the horizontal asymptote for the function h(x) = -e − 10.

Discover how to find the horizontal asymptote for the function h(x) = -e − 10. Learn about exponential functions and horizontal asymptotes, with a step-by-step breakdown of the solution. Ideal for students in Grades 11-12 studying calculus concepts.

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