Question

The cost for each car entering President George Bush Turnpike at Beltline road is $0.75. The equation that represents this relation is y = 0.75x, where x is the number of cars entering the turnpike at Beltline Road and y is the amount of money collected. Determine if this relation is a function. Explain.

Answer 1

From the definition of a function, a function associates every element of the domain to a unique element in the codomain.

In other words, if two elements are equal in the domain, then their images should also be equal.

Since, x represents the number of cars, we consider the universal set as N, the set of all natural numbers.

Let x, y ∈ N and x = y

Then, 0.75x = 0.75y

⇒ f(x) = f(y)

Therefore, images are equal, whenever elements are equal.

Hence, the function f(x) = 0.75x is a function. Also, note that the domain of the function is the set of all natural numbers and the range is the set of real numbers.