Homework SourseDetermine if the situation could be represented by a onetoon
Determine if the situation could be represented by a one-to-one function. Write a statement that describes the inverse function.
1. The number of miles n a marathon runner has completed in terms of the time in hours.
2. The depth of the tide d at a beach in terms of the time t over a 24-hr period.
Determine if the situation could be represented by a one-to-one function. Write a statement that describes the inverse function.
1. The number of miles n a marathon runner has completed in terms of the time in hours.
2. The depth of the tide d at a beach in terms of the time t over a 24-hr period.
1. The number of miles n a marathon runner has completed in terms of the time in hours.
2. The depth of the tide d at a beach in terms of the time t over a 24-hr period.
Solution
1). The function under normal conditions is one-to-one. As we cannot expect the runner to have completed the same number of miles at two different times during the race.
Hence Marathon function is one-to-one, and for any given time between start and finish, the function will return distance. The inverse function would have the distance as its argument, and would return the time at which that distance was reached.
2). The function would take time as its argument, and would return the tide depth. And the depth would be with respect to mean sea level. At any given location, barring extreme weather conditions, the tide level reaches zero at least three times per day, four on most days. The function would not be one-to-one.
