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? table a: x 20 25 30; d(x) 52 67.5 84. table b: d 52 67.5 84; v(d) 20 25 30. 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.

Explanation:

Two functions are inverses if for every ordered - pair (x, y) in one function, there is an ordered - pair (y, x) in the other function. In Table A, we have (x, d(x)) pairs and in Table B, we have (d, v(d)) pairs. When x = 20, d(x)=52 in Table A and when d = 52, v(d)=20 in Table B, and this pattern holds for all the values in the tables. Just because functions are increasing does not mean they are inverses.

Answer:

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.