Unit 05 · Family Guide

The Function Observatory

The central goal is to make students see a function as an input-output relationship with a domain—not merely as an equation to manipulate.

Unit Home

Useful prompts

  • What is the input? What is the output?
  • Can one input produce two outputs?
  • What inputs are actually allowed?
  • Do the table, graph, words, and rule agree?
  • What changed in the transformation?
  • Which piecewise rule owns the boundary?

Misconceptions to watch

  • Believing repeated outputs violate functionhood.
  • Reading f(x) as multiplication.
  • Dropping parentheses for negative inputs.
  • Ignoring contextual domain restrictions.
  • Checking a proposed rule against only one or two data points.
  • Reversing horizontal transformation directions.
  • Allowing overlapping piecewise boundaries with conflicting outputs.
  • Assuming every function automatically has an inverse function.

Evidence to preserve

One repaired function-test misconception, one domain/range explanation, pathway practice, Function Portfolio, Function Cartographer Boss Battle, and mastery result.