Part 2/6:
When ( a ) is a positive integer, the behavior of the graph changes based on whether ( a ) is odd or even. Let's analyze a few instances:
For ( a = 1 ): The graph is a straight line—essentially a linear function.
For ( a = 2 ): We observe a parabola opening upwards, reaching its minimum at the origin—indicating that all values are non-negative.
For ( a = 3 ): The resulting graph is asymmetric, displaying a classic cubic curve that descends in the negative range and ascends in the positive range.
For ( a = 4 ): This shape resembles the parabola again, similar to when ( a = 2 ).
For ( a = 5 ): The cubic pattern reasserts itself but steeper, similar to when ( a = 3 ).