The US has had a census every 10 years since 1780 If you tur

The US has had a census every 10 years since 1780. If you turned this into a function, what would you choose as the independent variable and what as the dependent variable. What is the domain? Describe a convenient co-domain. Recall that a number is rational if it is the ratio of two integers. If x is rational, set f(x) = 1. If x is not rational, set f(x) = 0. Is this assignment rule a function? If f is a function, what is its domain? range?

Solution

Since the population in a particular year depends upon the number of years since 1780,in the function y(t) ,

the independent variable, t = number of years since 1780 and

dependent variable, y = Population in that particular year.

Since the census is done in every 10 years, domain =[0,10]

The population of US in 1780 = 2.9 (millions)and

the population of US in 1790 = 3.9 (millions)

So we can define co-domain as [2, 4] (millions)