Math 1 · Unit 2 · Lesson 3 · part 3 of 6
A reasonable domain and range in a story
In a real situation, not every number makes sense as an input, and not every number can come out.
A reasonable domain and range in a story
In a real situation, not every number makes sense as an input, and not every number can come out. The inputs that make sense are the reasonable domain, and the outputs that can really happen are the reasonable range. Three examples, and the questions you ask to find them.
Time cannot be negative
A candle is 8 inches tall and burns 1 inch an hour: height = 8 − t. Can t be −2 hours? No, the candle has not been lit yet. Can t be 9 hours? No, it burned out at 8. So the reasonable domain (the inputs) is t is between 0 and 8, written 0 ≤ t ≤ 8. The heights that happen run from 8 down to 0, so the reasonable range (the outputs) is 0 ≤ height ≤ 8.
You cannot have half a person
A van seats 7. The number of riders n is a whole number from 0 to 7: the reasonable domain is n = 0, 1, 2, 3, 4, 5, 6, or 7. If each rider pays $4, the money collected is 4n, so the reasonable range is 0, 4, 8, 12, 16, 20, 24, or 28 dollars. Separate values, because this is discrete (only whole things), from Lesson 2.
A stadium holds only so many
Tickets are $20 and the stadium seats 5,000. Fans f can be any whole number from 0 to 5,000: the reasonable domain is 0 ≤ f ≤ 5000, whole numbers only. Money is 20f, so the reasonable range runs from 0 up to 20 × 5000 = 100,000: 0 ≤ money ≤ 100,000, in steps of 20.