Answer
(a) continuous
(b) continuous
(c) continuous
(d) discontinuous
(e) discontinuous
Work Step by Step
(a) continuous
Temperature normally changes gradually over time without sudden jumps to a higher or a lower temperature.
(b) continuous
As we move away from a location, we would expect a gradual change of temperature without sudden jumps to a higher or lower temperature.
(c) continuous
We would expect the land to change altitude gradually, and since the land is connected, a graph that follows the shape of the land would be continuous.
Note that there may appear to be discontinuities at sudden changes in altitude (e.g. a cliff). Whether or not these points show up as discontinuities (as opposed to rapid increases/decreases) depends on the "resolution" of the graph.
(d) discontinuous
Although the taxi fare may increase quite gradually as a function of distance, the taxi fare is measured in dollars and cents. Therefore, any increase in the fare would jump up in steps of one cent or more.
(e) discontinuous
While the light is turned on, the current would flow at a constant level. However, when the light is turned off, the current would suddenly jump down to zero. Over time, a graph of the current would show sudden jumps in the current when the light is turned on or off.
