To find $f(-4)$ given $f(x) = |-5 - 4x|$:

1. Substitute $x = -4$ into the function: $f(-4) = |-5 - 4(-4)|$

2. Simplify inside the absolute value: $= |-5 + 16|$

3. Calculate the expression inside the absolute value: $= |11|$

4. Since the absolute value of 11 is 11: $f(-4) = 11$

So, $f(-4) = 11$.

Would you like further details or have any questions?

Here are some related questions to explore:

1. How would you find $f(x)$ for any other $x$-value?
2. What is the range of $f(x) = |-5 - 4x|$?
3. How would the function change if it was $f(x) = -5 - 4x$ instead of $f(x) = |-5 - 4x|$?
4. What is the vertex of the function $f(x) = |-5 - 4x|$?
5. How would you find $f^{-1}(x)$ if $f(x) = -5 - 4x$ (without the absolute value)?

Tip: When working with absolute values, simplify the expression inside the absolute value before applying the absolute function.