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Topic 3.14 is about graphing polar functions r = f(theta).

  • Input/output: theta is angle from the positive x-axis; r is distance from the origin (3.14.A.1/A.3).
  • Construct: plot (theta, r) pairs or use technology to graph r = f(theta) (3.14.A.1).
  • Domain: restrict theta to show only the portion you need (3.14.A.2).

Why It Matters

Polar graphs describe circles, petals, cardioids, and other paths naturally tied to angle and distance.

How Families Can Help

  • Ask: "What angle? What distance from the origin?"
  • Sketch a few table points before the full curve.
  • Discuss why a problem might show only part of the graph.

What Not to Do

  • Do not plot polar graphs on ordinary x-y axes without converting.
  • Do not treat x as the input for r = f(theta).
  • Do not ignore a stated theta window.

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