Exam Strategy

Readiness Check

• Identify degree and leading coefficient (even from nonstandard order).
• State both limits: $x\to\infty$ and $x\to-\infty$.
• Use leading-term dominance language.
• Match the four cases: even/odd × positive/negative leading coefficient.

Before the Exam

1. Drill the four prototype graphs: $\pm x^2$, $\pm x^3$. 2. Expand or rewrite messy forms to spot the leading term. 3. Practice writing formal limit statements, not only “up on the right.” 4. Contrast: local turns (1.4) do not change end behavior.

During Multiple Choice

• Find $a_n$ and $n$ first; ignore constant and linear clutter.
• Even degree → same behavior on both ends; odd → opposite.
• Positive $a_n$ → right end up for the odd case; both up for even.

During Free Response

1. Name degree and leading coefficient. 2. Write both limits with correct $\infty/-\infty$. 3. Add one dominance sentence: leading term dominates for large $|x|$. 4. Optional verbal: “falls left, rises right,” etc., matching the limits.

Common Traps

• Using the constant term or a visible “first” term that is not leading.
• Describing only the right end.
• Letting a local max/min override end-behavior conclusions.

60-Second Checklist

• Leading term identified?
• Even or odd degree?
• Sign of $a_n$?
• Both limits written?