Math PicnicEvery sheet is a promise

Domain and range from a story worksheets

In a story, the domain is decided by the situation. These free printable worksheets give a short story about a tank, a jar of money or a trip and ask which input and output values make sense, with an answer sheet.

Customize Save as PDF I want another one

If they get stuck

See it worked step by step →
Domain and range from a story
Domain and range from a story worksheet — Tanks, jars and trips, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Time starts at zero and stops when the story does. If a tank fills at 5 gallons a minute for 12 minutes, then t runs from 0 to 12, even though the rule w = 5t would happily take any number at all. The equation does not know about the tank. Deciding what the numbers mean is the student's job, and it is exactly what the standard asks for.

Why this sheet works

The range comes from the domain. Work out the output at each end of the story, which here gives 0 gallons and 60 gallons, and the amount passes through everything in between. In a story that starts with money already in the jar, the range does not start at 0, and that is a common slip.

How this one works

A tank fills at 2 gallons a minute for 15 minutes. w is the water in it after t minutes.

Domain:0 ≤ t ≤ 15
Domain:0 ≤ t ≤ 15
Range:0 ≤ w ≤ 30
  1. The domain is every t value the function uses. t starts at 0, because time cannot be negative here, and stops at 15, when the story ends.
  2. The range is every w value it reaches. Find w at each end. It is 0 at one end and 30 at the other, and it passes through everything between.

Pick another skill