To evaluate the function $f(x) = -3e^x - 1$ at $x = -5$, substitute $-5$ for $x$ in the equation:

$f(-5) = -3e^{-5} - 1$

1. Calculate $e^{-5}$, where $e \approx 2.71828$.

2. Multiply the result by $-3$.

3. Subtract $1$.

Let's go through the calculation:

$e^{-5} \approx 0.0067$

Then:

$f(-5) = -3 \times 0.0067 - 1$ $f(-5) \approx -0.0201 - 1$ $f(-5) \approx -1.0201$

Thus, the answer is:

$f(-5) \approx -1.0201$

Would you like further details or have any questions?

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Here are some related questions to further explore:

1. How would the function change if the exponent were positive?
2. What is the effect of changing the coefficient from $-3$ to another number?
3. How does the function behave as $x \to \infty$?
4. What is the result of $f(x)$ when $x = 0$?
5. How would you graph this function, and what key features would it have?

Tip: Remember that $e^x$ grows quickly for positive $x$ but decays rapidly for negative $x$.