Short Answer 
The function is a piecewise function defined as f(x) = x + 3 for x < 0 and f(x) = 3 for x ‚â• 0. The graph visually represents this behavior with an upward slope for negative x values and a horizontal line for zero and positive values, confirming that the correct option is B.
Step 1: Identify the Function
The function is defined as a piecewise function that has two different expressions based on the value of x. The function is represented as:
- f(x) = x + 3, when x < 0
- f(x) = 3, when x ‚â• 0
This indicates that for negative values of x, the output increases linearly, while for zero and positive values, the output remains constant at 3.
Step 2: Analyze the Graph’s Behavior
The graph consists of two connected lines that illustrate the function’s behavior visually. The first line:
- Starts at the point (-5, -2) and slopes upward to (0, 3), representing x + 3.
From (0, 3) onwards, the second line extends horizontally, indicating a constant output of 3 for any value of x that is greater than or equal to 0.
Step 3: Confirm the Correct Option
Given the analysis of the function and the graph’s representation, we can validate the answer by matching it with the provided options. The correct choice is:
- B: f(x) = { x + 3, if x < 0; 3, if x ‚â• 0 }
This option accurately reflects the observed behavior of the graph, confirming it as the correct function based on the two conditions for x values.