Question

The minimum breaking distance d in feet for a typical vehicle can be modeled with the equation d(v) = 0.045v2, where v is the vehicle's speed in miles per hour. The minimum braking distance for a vehicle with new tires at optimal inflation is d(v) = 0.039v2. What kind of transformation describes this change from d(v) = 0.045v2 to d(v) = 0.039v2, and what does this transformation mean?
a.Horizontal compression by a factor of 13/15; the braking distance will be more with optimally inflated new tires than with tires having more wear.
b.Horizontal compression by a factor of 13/15; the brakin

Answer 1

To find the kind of transformation that describes this change from d(v) = 0.045v2 to d(v) = 0.039v2, find the relation between the two functions:

0.045/.039 = 45/39 = 15/13

The you have to multiply the first function times 13/15 to transform it to the second function.

When you multiply by a factor less than one you are compressiong the function vertically (if you multiply by a factor greater than 1 you are stretching vertically).

On the other hand, that the distance to stop the minimum braking distance will be smaller with the second function.

Then, the answer is that the transformation is a vertical compression by a factor of 13/15 and the braking distance will be less with optimum new tires than with tires having more wear.