Let’s solve the problem step by step.

The function given is:

$f(x) = -2x - 8$

We need to find $f(-5)$, which means substituting $x = -5$ into the function.

Step 1: Substitute $x = -5$ into $f(x)$

$f(-5) = -2(-5) - 8$

Step 2: Simplify the expression

$f(-5) = 10 - 8$

$f(-5) = 2$

Final Answer:

The value of $f(-5)$ is 2, so the correct option is:

$\boxed{2}$

Would you like a deeper explanation or help with other questions? Here are 5 related questions to expand your understanding:

1. How would the function change if the coefficient of $x$ were 3 instead of -2?
2. What is the value of $f(0)$ for this function?
3. How do we interpret the slope ($-2$) of the function geometrically?
4. What would happen to the graph if the constant term $-8$ were changed to $-10$?
5. How can you determine where $f(x) = 0$?

Tip: Always substitute carefully and simplify step-by-step to avoid calculation errors!