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Algebra 1 9-12 / Week 03 / Loft Day
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Week 03 · Functions

Loft Day

Loft Day: guess the rule
// One input, exactly one output
⏱ about 20 min

Loft Day: Guess the Rule

Saturday the crank box sits in the middle of the Loft table and the family gathers with index cards.

"Guess the rule," Comet says. "Feed in a number, get a number back. Say the rule when you know it."

A cousin feeds in 2 and gets 7. Then 5 and gets 13. "Times 2 plus 3!"

"Test it," Wren says. "What do you notice if you feed in 10?" The card comes back 23. "Confirmed."

Nova hovers above the box, her light dimmed to a hint. "Would you like a hint? Write it as g(x)."

"g(x) = 2x + 3," the cousin writes. "So g(10) = 23."

"Now you be the box," Comet says. "Pick a rule and we guess."

  1. A function gives exactly one output for each input in its domain.
  2. Domain in, range out.
  3. f(x) is the output of f at x. f(3) = 11 means 3 goes in and 11 comes out.
  4. The situation sets a sensible domain.
  5. A table, diagram or graph is a function only if no input has two outputs.
◇ FAMILY GUESS-THE-RULE
One person is the box and writes a secret rule such as × 2 + 3 on a hidden card.
Everyone else feeds in inputs on cards and records each pair in a table.
When someone guesses the rule, test it with two new inputs before calling it confirmed.
Write the rule in function notation and trade roles. Then try a rule that is not a function and watch the table.
For a grown-up
A grown-up cuts any slots in the box and keeps the scissors.
Keep cards on the table so nobody slips on paper.
A wrong guess is useful: feed in one more input and let the table decide.
LOFT DAY CHECK
  • Read the question.
  • Tap your answer.
The cousin's rule was g(x) = 2x + 3. What is g(10)?
With g(x) = 2x + 3, what is g(7)?
The family table: (2, 7), (5, 13), (10, 23), (2, 7). Is it a function?
With g(x) = 2x + 3, what is g(0)? Type the number.
WHY THIS EXERCISEEvery input in the domain, even 0, gets exactly one output.
Draw the family table with its input column and output column, and write the rule in function notation below it.
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