Exam Strategy

Readiness Check

You are ready when you can:

• Write the inverse of $y=b^x$ as $y=\log_b x$.
• Swap table/graph pairs correctly.
• Verify inverses by composition.
• Describe the additive/multiplicative growth contrast.
• Sketch the reflection over $y=x$.

On the AP Exam

• MCQ: identify inverses, match graphs, read swapped pairs, growth language.
• FRQ: construct log inverse of an exponential, justify with pairs or composition.
• Skills: 1.C construct functions; 2.B equivalent representations.

Tactics

1. Start from $y=b^x$, swap $x$ and $y$, solve: $x=b^y\Rightarrow y=\log_b x$. 2. Check Dom$(\log_b)=(0,\infty)$ and Range $=\mathbb{R}$. 3. Use one known point on $b^x$ to get a point on $\log_b$. 4. Say growth in matched sentences: "add input / multiply output" vs "multiply input / add output." 5. Reflect carefully over $y=x$, not the axes.

Common Traps

• Inverse written as reciprocal or $x^b$.
• Wrong domain for the log.
• Mixing exponential and log growth descriptions.
• Forgetting coefficient $a$ in $a\log_b x$ when given.

Quick Checklist

• [ ] Inverse form correct
• [ ] Pairs swapped
• [ ] Composition verified
• [ ] Growth language accurate
• [ ] Reflection over $y=x$