Question

In a physics class, the teacher proposes that the velocity of a car in miles per hour and the stopping distance in feet are represented by inverse functions.Assuming this is true, which graph includes a pair of functions for a specific velocity function and the corresponding stopping distance that can be verified as inverses?

Answer 1

The velocity of a car and the stopping distance are inverse functions. An example of a pair of inverse functions is v(x) = 60/x and d(x) = 60/v.

Step-by-step explanation:

In this case, the velocity of a car in miles per hour and the stopping distance in feet are represented by inverse functions. This means that as the velocity increases, the stopping distance decreases, and as the velocity decreases, the stopping distance increases. An example of the pair of inverse functions for this situation would be:

Velocity function: v(x) = 60/x (where v(x) represents the velocity in miles per hour and x represents the stopping distance in feet)

Stopping distance function: d(x) = 60/v (where d(x) represents the stopping distance in feet and v represents the velocity in miles per hour)

These functions are inverses of each other because if you substitute the value of x from the velocity function into the stopping distance function, or vice versa, you will get back the original input value. For example, if you substitute x = 60 into the velocity function, you will get v = 1, and if you substitute v = 1 into the stopping distance function, you will get x = 60.