Chapter 4.4, Problem 33PPE

To determine

Whether the graph is discrete.

Answer to Problem 33PPE

The definition the continuous graph, above graph is continuous

Explanation of Solution

Given information:

The graph shows the distance $d$ of running, in miles, as a function of time $t$ in minutes, during a 5-mi run.

One says that graph is discontinuous at $d=5$ , so the graph is discrete.

Graph is given as

  

Calculation:

Consider below graph it shows that distance $d$ run, in miles, as a function of time $t$ , in minutes, for 5 minutes run. In below graph horizontal axis represents time and vertical axis represents distance run. Graph is as follows -

  

A continuous graph represents a function which can be evaluated at any point along the graph line. Observe the above graph. For any instance of time $t$ , now able to find the corresponding distance. Since this run is for 5 miles, the graph stops at $d=5$ .

Thus, by the definition the continuous graph, above graph is continuous.