Math 1 · Unit 2 · Lesson 2 · part 4 of 6
Continuous or discrete: when to connect the dots
So should you always connect the dots?
Continuous or discrete: when to connect the dots
So should you always connect the dots? Only when the in-between inputs are real. That depends on the story, and it gives us two words.
Continuous: connect the dots
A tub fills at 3 gallons every minute. After t minutes it holds y = 3t gallons. Can t be 1.5 minutes? Yes: a minute and a half is a real amount of time, and the tub really does hold 4.5 gallons then. Every in-between input is real, so the graph is a solid line.
Discrete: leave the dots separate
Tickets cost $3 each. For n tickets you pay y = 3n dollars. Can n be 1.5 tickets? No: you cannot buy half a ticket. There is no in-between input, so there is no in-between point. The graph stays as separate dots, and you do not connect them.
The question to ask. Can the input be any number, including the ones in between? Then it is continuous, and you connect the dots. Can the input only be whole things, like people, tickets, or cars? Then it is discrete, and the dots stay separate.