Suppose a second degree polynomial function f(x, y, z)
= x2 + y2 – z2, describes the temperature at a point in 3D
space.

If C is a constant temperature, then the equation f(x, y, z) = C
generates the graph

Of a 3D level surface called an isotherm. Three distinct isothermal
surfaces are depicted in the figure below. identify which surface
represents a temperature below zero, above zero and equal to zero
and ×explain each identification using well written English
sentences and algebra.

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