Exam Strategy
Readiness Check
You are ready when you can:
- Evaluate $(f\circ g)(x)$ from formulas, tables, and graphs.
- State composite domain restrictions.
- Build $f(g(x))$ by substitution.
- Decompose a function into two simpler functions.
- Explain why order matters.
On the AP Exam
- MCQ: evaluate composites, identify domain, compare $f\circ g$ vs $g\circ f$.
- FRQ: construct composite models, decompose, connect to transformations.
- Skills: 1.C construct functions; 2.B equivalent representations.
Tactics
1. Always identify inner ($g$) and outer ($f$) in $f\circ g$. 2. Domain: solve $x\in\text{Dom}(g)$ and $g(x)\in\text{Dom}(f)$. 3. Tables: read $g(x)$ first column pass, then $f(\text{that value})$. 4. Graphs: follow output of $g$ to input of $f$. 5. Decompose by asking what operation happens first to $x$.
Common Traps
- Reversing order.
- Multiplying instead of composing.
- Missing domain from inner output (e.g., $\log(g(x))$ requires $g(x)>0$).
- Incorrect decomposition that fails recomposition check.
Quick Checklist
- [ ] Inner function evaluated first
- [ ] Domain checked
- [ ] Formula simplified if asked
- [ ] Order stated when comparing composites