AP Precalculus · Summary

Unit 2 summary

1. Arithmetic sequences add a constant difference and are linear; geometric sequences multiply by a constant ratio and are exponential.
2. In $f(x) = ab^x$, a is the value at x = 0 and b is the factor per unit of x; $b - 1$ as a percent is the rate per unit.
3. To fit $ab^x$ to two points, divide the outputs to find b, then use a point to find a.
4. $f(g(x))$ applies g first. The inverse undoes f, swaps inputs and outputs, and exists only when f is one-to-one.
5. $\log_b c = a$ means $b^a = c$. Logs turn products into sums, quotients into differences and powers into factors.
6. Solve exponential equations by isolating the power and taking a log; check log-equation answers for extraneous ones.
7. Exponential data are linear on a semi-log plot: the slope is $\log b$ and the intercept is $\log a$.