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Q. Draw
- Understand Function Behavior: Understand the function to be graphed.The function is a two-variable function, which means its graph will be a three-dimensional surface. The function is the product of and , which are both parabolas in their respective variables. The graph of this function will show how the product of these two parabolas behaves in three-dimensional space.
- Identify Key Features: Identify the key features of the graph.Since both and are always non-negative, their product will also be non-negative. This means the graph will lie in the region where is greater than or equal to zero. Additionally, the graph will be symmetric with respect to both the -axis and the -axis because squaring a number always gives a non-negative result, regardless of whether the original number was positive or negative.
- Determine Origin Behavior: Determine the behavior of the function at the origin.At the origin, where and , the function will be equal to . This is because any number multiplied by zero is zero. Therefore, the graph will touch the origin.
- Sketch Graph: Sketch the graph.To sketch the graph of , we can start by considering lines where either or . Along these lines, the function will be zero since one of the factors will be zero. As we move away from these lines, the value of the function will increase since both and will be positive and increasing. The graph will form a sort of ＂ridge＂ or ＂mountain＂ shape that rises as we move away from the -axis and -axis, with the highest points moving out diagonally from the origin.
