Question

A function f is a relation in which each element of the domain corresponds exactly to one element of the range. Which of the following best describes the nature of a function?

a) Each element in the domain corresponds to multiple elements in the range.

b) Each element in the domain corresponds to exactly one element in the range.

c) Elements in the domain and range are unrelated.

d) The range is empty.

Answer 1

The nature of a function is that each element in the domain corresponds to exactly one element in the range, as described by option b). This definition applies regardless of the context, including both simple mathematical functions or economic models.

Step-by-step explanation:

The nature of a function is best described by option b) Each element in the domain corresponds to exactly one element in the range. This is a fundamental definition of what a function is in mathematics. Consider a simple function f(x) for 0 ≤ x ≤ 20. If the graph of f(x) is a horizontal line, it means that for every value of x within the domain, there is exactly one corresponding value in the range. So, regardless of the value of x between 0 and 20, there is one and only one value f(x) will take on. Similarly, in economic models, functions describe relationships where a variable is dependent on another, like Professor = Adam Smith or Friends = Bob + Shawn + Margaret. The relationship defined by a function is always singular under its domain.