Find the positive area of the function
Find the positive area of the function
To determine where the function is positive, we consider the nature of this parabolic graph, which opens upwards.
Step 1: Recognize that the function outputs non-negative values for any real number . The graph of this function is a U-shaped parabola.
Step 2: Analyze the values of the function:
- For , .
- For , , because squaring any non-zero real number results in a positive value.
Therefore, the function is positive for all except at , where it is zero.
Step 3: Based on the comparison given in the choices, and our calculation, the area of interest is positive for .
Thus, the solution to the problem is that the positive area occurs for .