If Paul is driving at a constant rate of 65 miles per hour, the distance he travels (d) is a function of the time he drives (t). If Paul can drive at the most for 4 hours list the reasonable domain and range of this function?
Well, if Paul is driving at a constant rate of 65 miles per hour for a maximum of 4 hours, the reasonable domain would be 0 ≤ t ≤ 4. We want to avoid any negative time or time larger than 4 hours, because that would make no sense in this context.
As for the range, the distance Paul travels (d) would be directly proportional to the time (t) he drives. So, we can calculate the range by multiplying the maximum time (4 hours) by the rate (65 miles per hour), giving us a range of 0 ≤ d ≤ 260 miles.
Just remember, these values are within the reasonable limits of this scenario. Paul could very well decide to stop for a snack or take a break, so he might not actually reach the maximum range. But that's a decision for Paul to make, not for the math!
To determine the reasonable domain and range of this function, let's analyze the given information.
Domain refers to the set of all possible input values (independent variable), while range refers to the set of all possible output values (dependent variable).
In this case, the independent variable is the time Paul drives (t), and the dependent variable is the distance he travels (d).
Given that Paul can drive at most for 4 hours, we need to consider the reasonable range of values for t.
Domain (reasonable range for t): Since Paul can drive for a maximum of 4 hours, the reasonable domain for this function would be [0, 4]. This means that the time Paul drives must be between 0 and 4 hours, including both endpoints.
To determine the reasonable range for d, we need to consider the relationship between speed, time, and distance.
The formula for distance (d) is given by d = speed * time.
Given that Paul is driving at a constant rate of 65 miles per hour, we can use the formula to calculate the reasonable range for d.
Range (reasonable range for d): Since the speed is constant at 65 miles per hour, the range for d will depend on the time (t) Paul drives. Multiplying the speed (65 mph) by the maximum time (4 hours), we can find the maximum distance:
d = 65 * 4 = 260 miles
Therefore, the reasonable range for d would be [0, 260]. This means that the distance Paul travels can range from 0 miles (when t=0) to a maximum of 260 miles (when t=4).
In conclusion, the reasonable domain for this function is [0, 4] and the reasonable range is [0, 260].
To determine the reasonable domain and range of the function, we need to consider the given information. We know that Paul is driving at a constant rate of 65 miles per hour, and he can drive at most for 4 hours.
Domain represents the set of all possible input values for the function, which in this case would be the time Paul drives. Given that he can drive for a maximum of 4 hours, the reasonable domain for this function would be from 0 to 4, inclusive. Therefore, the domain is:
Domain: 0 ≤ t ≤ 4
Range represents the set of all possible output values for the function, which in this case would be the distance Paul travels. Since Paul is driving at a constant rate of 65 miles per hour, we can calculate the range by multiplying the rate (65 mph) by the time (t). The range would be all the possible distances Paul can travel within the given time.
Considering that Paul can drive for a maximum of 4 hours, the range of this function would be:
Range: 0 ≤ d ≤ (65 × 4) = 260 miles
Therefore, the reasonable domain is 0 ≤ t ≤ 4, and the reasonable range is 0 ≤ d ≤ 260 miles.
d = 65 t
t </= 4 seconds = domain
t = 0 ----> dist = 0
t = 4 ----> dist = 260
so range 0 </= d </= 260 miles