Evaluate the function. (Round your answer to four decimal places.)
f(x) = −9ex − 1,
for
f(−5)
f(−5) =

To evaluate the function \( f(x) = -9e^x - 1 \) at \( x = -5 \), substitute \( x = -5 \) into the function:

\[
f(-5) = -9e^{-5} - 1
\]

Now, calculate \( e^{-5} \):

\[
e^{-5} \approx 0.006737947
\]

So, substitute this into the equation:

\[
f(-5) = -9 \times 0.006737947 - 1
\]

\[
f(-5) \approx -0.060641523 - 1
\]

\[
f(-5) \approx -1.0606
\]

So, \( f(-5) \approx -1.0606 \) when rounded to four decimal places.

Would you like more details or have any questions?

Here are some related questions you might consider:

1. How does the base of the natural logarithm \( e \) affect the function?
2. What happens to \( f(x) \) as \( x \) becomes very large?
3. How would you differentiate \( f(x) = -9e^x - 1 \)?
4. What is the inverse function of \( f(x) = -9e^x - 1 \)?
5. How would the function change if the coefficient of \( e^x \) was different?
6. How does the constant term \( -1 \) influence the graph of the function?
7. How would you solve for \( x \) if \( f(x) = 0 \)?
8. What is the y-intercept of the function \( f(x) = -9e^x - 1 \)?

**Tip:** When dealing with exponential functions, remember that small changes in the exponent can result in large changes in the value of the function.

Learn how to evaluate the exponential function f(x) = -9e^x - 1 at x = -5 with detailed steps and calculations. This problem involves exponential functions, natural exponentials, and function evaluation techniques. Suitable for advanced high school students in Grades 11-12.

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