Question

Table A represents the function that models the stopping distance in feet of a derby car, d(x), based on the velocity in miles per hour of the car, x.

Table B represents the function that models the velocity of a car, v(d), in miles per hour based on distance in feet it took the car to stop, d.





When verifying the relationship between the functions using the values in the tables, what conclusion can be made?

Since the functions in both tables are increasing, they are inverses.
Since the functions in both tables are increasing, they are not inverses.
Since for each ordered pair (x, y) for one function there is an ordered pair (y, x) for the other function, the functions are inverses.
Since for each ordered pair (x, y) for one function there is an ordered pair (y, x) for the other function, the functions are not inverses.

Answer 1

Since for each ordered pair (x, y) for one function there is an ordered pair (y, x) for the other function, the functions are inverses.

Reason: Inverse functions swap inputs and outputs; showing each (x,y) in one table corresponds to (y,x) in the other verifies they are inverses. Monotonicity alone does not guarantee inverse relationship.