To find $f(-4)$ given the function $f(x) = 4x + 1$, follow these steps:

1. Substitute $x = -4$ into the function $f(x)$. $f(-4) = 4(-4) + 1$

2. Multiply: $f(-4) = -16 + 1$

3. Add the numbers: $f(-4) = -15$

So, $f(-4) = -15$.

Would you like more details or have any questions? Here are some related questions:

1. How do you find $f(0)$ for the same function $f(x) = 4x + 1$?
2. What is the graph of the function $f(x) = 4x + 1$?
3. How would you solve $f(x) = 0$ for the given function?
4. What is the slope and y-intercept of the function $f(x) = 4x + 1$?
5. How do you find the inverse of the function $f(x) = 4x + 1$?

Tip: When substituting values into a function, ensure you substitute correctly and follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).