For a signum function f(x), the value of f(x) at x = -4 is

Options

A. `-1`
B. 0
C. `-4`
D. 4

Answer

To find the value of the signum function \( f(x) \) at \( x = -4 \), we follow these steps:

### Step 1: Understand the Signum Function
The signum function, denoted as \( \text{sgn}(x) \), is defined as follows:
- \( \text{sgn}(x) = -1 \) if \( x < 0 \)
- \( \text{sgn}(x) = 0 \) if \( x = 0 \)
- \( \text{sgn}(x) = +1 \) if \( x > 0 \)

### Step 2: Identify the Value of \( x \)
In this case, we have \( x = -4 \).

### Step 3: Determine the Condition of \( x \)
Now, we need to check which condition \( x = -4 \) satisfies:
- Since \( -4 < 0 \), we fall into the first condition of the signum function.

### Step 4: Apply the Definition
According to the definition of the signum function:
- Since \( x = -4 \) is less than 0, we have:
\[ f(-4) = \text{sgn}(-4) = -1 \]

### Conclusion
Thus, the value of \( f(x) \) at \( x = -4 \) is:
\[ \boxed{-1} \]

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