How To Find Domain And Range Of Multivariable Functions

Level curve

It may come as a surprise to find that the problem of representing three-dimensional surfaces on paper is familiar to most people (they just don’t realize it). Topographic maps, such as those shown in Figure (PageIndex {3}), represent the Earth’s surface by indicating points of the same elevation as contour line. The heights are marked equally spaced; in this example, each thin line represents a change in elevation in 50 ft increments, and each thick line represents a 200 ft change. When the lines are drawn close together, the elevation changes rapidly (since one doesn’t have to travel far to gain 50 ft). When roads are far apart, such as near “Aspen Campground,” the elevation changes gradually as people have to walk further to gain 50 ft.Figure (PageIndex {3}): A topographic map that displays elevation by plotting contour lines, with the elevation being constant. Given a function (z = f (x, y)), we can draw a “topographic map” of (f ) by plotting level curve (or, contour line). The level curve at (z = c) is a curve in the plane (x) – (y) such that all points ((x, y)) on the curve, (f(x, y) = c) . : how to find the domain and range of multivariable functions Read more: How to make a watering can with lights When plotting level curves it is important that the values (c) be spaced evenly to get a look most profoundly about how fast the “altitude” is changing. Examples will help one understand this concept.

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