Question

Which of the following are examples of a function? Justify your answers.

i. The assignment of each rational number to the product of its numerator and denominator.

Answer 1

Answer: Hello there!

The relation of two quantities is a function only when for each point in the domain, there is only one point associated on the codomain (or range).

this means that, for a point x in the domain; if f(x) = y1 and f(x) = y2, this means that y1 = y2.

now we have:

"The assignment of each rational number to the product of its numerator and denominator."

here you are "assigning" rational numbers, to the product of their parts, then the rational numbers are the range, and the domain is the product of two integer numbers, so the domain is the set of all integer numbers.

now suppose we have the numer 6, and we know that 6 = 2*3, then:

f(6) = 2/3 or f(6) = 3/2

so we can asociate the numer 6 in the domain, with two numbers in the codomain, so this relation is not a function.