Exam Strategy

Readiness Check

You are ready when you can (1) write $a$ and $b$ from $f(x)=ab^x$, (2) classify growth/decay, (3) state domain and end behavior, (4) describe monotonicity and concavity, and (5) deny global extrema/inflection on $\mathbb{R}$.

Prep Sequence

1. Ten classify growth/decay drills. 2. Five limit-statement items. 3. Five ratio-table verifications. 4. Three "extrema on $\mathbb{R}$?" questions. 5. Two shifted-form reads ($a b^{x-h}$).

On the Exam

• Start with $f(0)=a$.
• Compare $b$ to 1 for growth vs decay.
• For limits: track whether outputs blow up or approach 0.
• If asked about max/min on all reals: "none" unless a closed interval is specified.
• Proportional outputs over equal $\Delta x$ => exponential.

Common Traps

• Calling decay "negative slope linear."
• Missing that $0<b<1$ still means exponential decay, not "not exponential."
• Forgetting $\lim_{x\to-\infty} b^x$ when $b>1$ is 0.
• Claiming an inflection point.

Quick Checklist

• [ ] $a\neq 0$, $b>0$, $b\neq 1$
• [ ] Growth/decay correct
• [ ] Domain all reals stated
• [ ] Limits/end behavior stated
• [ ] No unjustified extrema/inflection on $\mathbb{R}$