Alex drives at a speed 75 mph. Write a function showing the dependence of the distance (D) covered by Alex in t hours. Find the domain and range of the function.

Given Information:

Speed = v = 75 miles per hour

Time = t hours

Required Information:

Distance function = ?

Domain = ?

Range = ?

Answer:

Distance function = D = 75t miles

Domain = (0 ≤ t ≤ ∞)

Range = (0 ≤ D ≤ ∞)

Step-by-step explanation:

Alex is travelling at a speed 75 miles per hour for t hours then the distance covered is

D = vt

D = (75 miles/hour) (t hour)

hour cancels out

D = 75t miles

Therefore, Alex covers a distance of 75t miles.

Domain:

The domain is all those possible values of time t for which we get a real output value of distance D.

Since time cannot be negative in this case the domain will be

Domain = (0 ≤ t ≤ ∞)

Range:

The range is all those values of distance D after we substitute all the possible values of time t.

Range = (0 ≤ D ≤ ∞)

75t; range is 0≤D≤75t

Step-by-step explanation:

Speed is defined as the change in distance of a body with respect to time.

Speed = Distance/Time

Given speed = 75mphr

Time covered by Alex = t hours

Distance covered by Alex can be expressed in term of t as;

Distance = (75meter/hr) * thr

Distance = 75m/hr * t hr

Distance = 75t meters

If the time T can take any value between 0 and t, range of the time will be 0≤T≤t.

Therefore the range of the distance will be 0≤D≤75t where;

D = 0 at T = 0 and

D = 75t at T = t