Final answer:
The equation representing driving 330 miles towards home at 55 mph is d = 330 - 55t. The domain is all non-negative times (t ≥ 0), and the range is all distances from home between 0 and 330 miles (0 ≤ d ≤ 330).
Step-by-step explanation:
Calculating Distance, Time, and Speed
To represent the situation of driving 330 miles toward home at an average speed of 55 mph, we can use the formula distance = rate × time. In this context, distance d is the number of miles away from home, rate r is the average speed of 55 mph, and time t is the time in hours. If we let t represent the hours it takes to drive home, the equation would be d = 330 - 55t.
The domain of this function is the set of all possible values of t that makes sense in this context, which is t ≥ 0 because you cannot drive for negative time. The range of this function as determined by the domain is the possible distance from home, which is 0 ≤ d ≤ 330 miles because you cannot be more than 330 miles away if you are driving towards home.