Question

Explain why each function is continuous or discontinuous. (a) The outdoor temperature as a function of longitude, latitude, and time is ---Select--- . Small changes in longitude, latitude or time can produce ---Select--- changes in temperature. (b) Elevation (height above sea level) as a function of longitude, latitude, and time is ---Select--- . Small changes in longitude, latitude, or time can produce ---Select--- changes in elevation. (c) The cost of a taxi ride as a function of distance traveled and time is usually ---Select--- . Small changes in distance traveled or time can produce ---Select--- changes in cost.

Answer 1

Answer:

Continuous or Discontinuous Functions

(a) The outdoor temperature as a function of longitude, latitude, and time is ---continuous--- . Small changes in longitude, latitude or time can produce ---continuous--- changes in temperature.

(b) Elevation (height above sea level) as a function of longitude, latitude, and time is ---continuous--- . Small changes in longitude, latitude, or time can produce ---continuous--- changes in elevation.

(c) The cost of a taxi ride as a function of distance traveled and time is usually ---continuous--- . Small changes in distance traveled or time can produce ---continuous--- changes in cost.

Explanation:

A continuous function does not experience discontinuities.  Some human attributes like height, weight, temperature, and body colors are continuous variations.   Discontinuous variables have distinct categories that are different.  Examples are sex, blood group, etc.  Discontinuous functions bear "either or" properties.