Functions

Step 1: Analyze the function.
The function involves the absolute value of , which affects its behavior based on the sign of . The function can be rewritten as:
Thus, for , , and for , .

Step 2: Identify the correct graph.
From the given function, we see that the graph will be a piecewise constant function:
For , the function value is , so the graph will be a horizontal line at for positive .
For , the function value is , so the graph will be a horizontal line at for negative .

Step 3: Compare with the options.
Option (A) matches this behavior, where for , , and for , . The graph shows this exact pattern, making it the correct choice.