Final answer:
A contour map for the function f on the specified square shows the level curves of the function. These curves map out constant values of f over the square and are different from the gradient, partial derivatives, or integral of the function.
Step-by-step explanation:
The question pertains to understanding what is represented on a contour map for a function f over a specified square domain. On such a map, option 1 is correct: The level curves of the function f are shown. Level curves, also known as contour lines, are lines that connect points where the function has the same value, effectively mapping out constant values of f across the square domain. These curves give us a visual representation of how the function changes value over the area.
The gradient of the function f, which is option 2, is a vector representation of the rate of change of the function in the steepest direction and is not shown by contour lines. Option 3, the partial derivatives of the function f, are the slopes of the function in the x and y directions individually and are also not explicitly shown on a contour map. Finally, option 4, which refers to the integral of the function f, represents the accumulation of the function's values over a region and is traditionally represented by the area under a curve in a graph - not by contour lines.