If f(x) is a greatest integer function, then f(-2. 5) is equal to

Options

A. `-3`
B. `-2`
C. 2
D. 3

Answer

To solve the problem of finding \( f(-2.5) \) where \( f(x) \) is the greatest integer function, we follow these steps:

### Step 1: Understand the Greatest Integer Function
The greatest integer function, often denoted as \( \lfloor x \rfloor \), returns the largest integer less than or equal to \( x \).

### Step 2: Identify the Input Value
In this case, we need to evaluate \( f(-2.5) \).

### Step 3: Determine the Greatest Integer Less Than or Equal to -2.5
To find \( f(-2.5) \), we need to identify the largest integer that is less than or equal to -2.5.

### Step 4: Analyze the Integers Around -2.5
The integers around -2.5 are:
- -3 (which is less than -2.5)
- -2 (which is greater than -2.5)

### Step 5: Conclusion
Since -3 is the largest integer that is less than -2.5, we conclude that:
\[ f(-2.5) = -3 \]

### Final Answer
Thus, \( f(-2.5) \) is equal to -3.

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