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Function evaluation is a critical part of mathematics, especially when dealing with linear functions. At its core, evaluating a function simply means finding the output value for a particular input value. In our given example, we want to evaluate a linear function defined as \( f(x) = -4x \). To evaluate this function for a specific number like 3 or -1, you substitute these values into the function to find \( f(3) \) or \( f(-1) \), respectively. Be sure to carefully replace every occurrence of \( x \) in the function with your chosen number. With this in mind, function evaluation uses fundamental simplicity to derive an answer from a function for any chosen input.

The substitution method is straightforward but powerful. When you are given a function like \( f(x) = -4x \) and asked to find \( f(3) \) or \( f(-1) \), you use the substitution method. Here’s how it works:- Identify the value you need to substitute into the function.- Replace the variable \( x \) in the equation with this identified value.For example, to find \( f(3) \), substitute 3 in place of \( x \) in the equation, turning it into \( f(3) = -4(3) \). This demonstrates how substitution acts as a bridge in carrying numerical values into functions, helping find the right results.

Multiplication is a fundamental arithmetic operation, frequently used in algebra. Understanding how to multiply in algebra is key when evaluating functions like \( f(x) = -4x \). This function requires you to multiply the constant coefficient -4 by the input value you substituted for \( x \). Let’s consider these steps:- When substituting \( x = 3 \), perform the multiplication: \(-4 \times 3\). The product is -12.- When substituting \( x = -1 \), perform \(-4 \times -1\). The negatives cancel out, leaving the result as 4.It's important to remember that the signs matter. Multiplying two negative numbers results in a positive product, while a negative and a positive number produce a negative product. Recognizing this pattern is crucial for solving and understanding algebraic expressions.