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The depth of a lake at a center point is a function of the distance of that point from shore.
If you mean a straight path, rather than a strait path, then it is a ray.
A rational function is the quotient of two polynomial functions.
Typically, functions are graphed on x-y coordinates. A function of x means that for every x point, there must be a single y point. You can also many properties by graphing a function, such as the minimum and maximum points, slopes and inflection points, and the inverse of the function (y values plotted on x coordinate, and x values on y coordinate).
The shortest path is a line perpendicular to the given line that passes through the given point.