Exam Strategy
Readiness Check
- Find candidate zeros from the numerator.
- Exclude values that make the denominator zero.
- State domain restrictions clearly.
- For $r\ge 0$ / $r\le 0$, use zeros of both polynomials as interval endpoints/asymptotes.
Before the Exam
1. Drill: factor num and den; list domain exclusions; keep valid numerator zeros. 2. Drill: shared factor cases—candidate eliminated from zeros of $r$. 3. Build sign charts using num zeros + den zeros. 4. Match graphs: $x$-intercepts only where $r=0$ in domain.
During Multiple Choice
- Check domain before selecting a zero.
- “$x=a$ makes both zero” is usually not a zero of $r$.
- Inequality answers need all critical values from num and den.
During Free Response
1. Factor if helpful; solve $p(x)=0$. 2. State domain: $q(x)\ne 0$. 3. List zeros of $r$ with justification “in domain.” 4. For inequalities: list critical values from both polynomials, test intervals, conclude.
Common Traps
- Listing every numerator root automatically.
- Treating denominator zeros as zeros of $r$.
- Sign chart missing a denominator zero (missed asymptote barrier).
60-Second Checklist
- Numerator candidates?
- Domain filter applied?
- Inequality: both polynomials’ real zeros marked?