Question

The journey of a car travelling towards

Perth, Australia, can be expressed by the
relation d=-75t + 275, where d is the
distance from Perth in km and t is driving
time in hours.
a Is this relation a function? Justify your
answer.
b Rewrite the equation in functional
notation.
At the start of the journey, how far was
the car from Perth?
С
d What values of I do not make sense for
this situation?

Answer 1

a. The given equation is d = -75·t + 275 is a function

b. f(t) = -75·t + 275

c. 275 km

d. The situation does not makes sense for t > 11/2 hours.

Explanation:

a. Given that a relation is a functional relation if for each input of a member in the relation, there is only one output for the other member, therefore;

The given equation is d = -75·t + 275 is a function

As when t = 1, d = 200 km

b. The equation written in functional notation, f(t) is f(t) = -75·t + 275

c. At the start of the journey, t = 0

Therefore;

f(0) = -75×0 + 275 = 275 km

d. The values of t that do no make sense in the function are given as follows

0 = -75×t + 275

t = 275/75 = 11/3 = 3.67 hours

For times above 3.67, the distance becomes negative

Therefore, the situation does not makes sense for t > 11/2 hours.