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Common Mistakes

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Frequent Errors

1. Assuming one implicit equation means one function only (4.5.A.1). 2. Graphing only points from one explicit branch (4.5.A.3). 3. Not verifying candidate points in the equation (4.5.A.2). 4. Reversing co-variation: positive ratio misread as opposite change (4.5.B.1). 5. Using one distant point pair for local variation claim (4.5.B.1). 6. Missing horizontal interval when dy/dx = 0 locally (4.5.B.2). 7. Missing vertical interval when dx/dy = 0 locally (4.5.B.2). 8. Skipping technology when hand plotting is incomplete (2.B).

Why These Happen

Students prefer y = f(x) and underplot implicit relations.

How to Fix Them

  • Test points before plotting.
  • Solve for y and y = ... separately when two branches exist.
  • Use nearby points for Delta y / Delta x.

Avoidance Scripts

  • "Satisfy the equation first."
  • "One solve, one branch."
  • "Nearby points for together/opposite."

Quick Self-Check

  • Did I check the point in the equation?
  • Did I note all visible branches?
  • Did I use nearby points for co-variation?

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