What are the possible amounts of money you can have if you only have quarters? What is the smallest unit you can measure distance?
See solution.
Practice makes perfect
Let's look at each of these functions individually.
Function A
We have a jar full of quarters and want to know how much money we have based on the number of quarters we have. Each quarter is worth 25 cents, or $0.25. If we let the number of quarters be x, then we can write the total amount of money, in dollars, as an expression.
0.25xSince we can only have whole quarters, the input values for x will only be whole numbers. The domain will then be all non-negative integers.
Function B
We need to consider that the distance changes based on how much time has passed. We know that time is a continuous quantity and that it can never run backwards. Therefore, the function's domain is continuous and can be any value greater than or equal to zero.
t≥0
Zero is whenever we started keeping track of the amount of time that has passed. Since we do not know how far home is, we cannot find a maximum value.
Comparing the Domains
Even when both domains are made of numbers greater than or equal to 0 the domain of Function A is discrete, as it is made of integers. The domain of Function B is continuous because it is made of real numbers.
