Answer:
D) The situation could be represented by a one-to-one function if the runner does not stop to rest. The inverse function would represent the time in hours for a given number of miles completed.
Explanation:
Given:
Input: time t (in hours) is the independent variable.
Output: miles n is the dependent variable.
When the input value is time and the output value is miles, it doesn't matter if the runner stops once, at least once, only once, or not at all - the relation will always be a one-to-one function.
(See the red line on the attached graph).
Inverse:
Input: miles n is the independent variable.
Output: time t (in hours) is the dependent variable.
The inverse of a graphed function is its reflection in the line y = x.
Therefore, if the runner stops for any period of time, when this part of the graph is reflected in the line y = x, it becomes a vertical line, and therefore the inverse is no longer a one-to-one function.
(See the blue line on the attached graph).
Therefore, the situation can only be represented by a one-to-one function if the runner does not stop to rest, as then the inverse is also a function.