About Test 2

  • Covers chapters 4, 5, 6
  • You may use pencil, pen, non-graphing calculator (and not Wolfram Alpha)
  • You may bring notes on function shifts / stretches / reflections!
  • During class (in SC 107) on Wednesday, March 9. You may start as early as 7:45 am!
  • A chance to re-submit parts of the exam afterwards--to be due on Friday.

Review

  • Know properties of logarithms and exponentials, e.g. $\log(a*b)=\log(a)+\log(b)$, $e^a/e^b=e^{a-b}$, $\ln(a^t)=t\ln(a)$, etc.
  • Know about how to use the fact that logarithms and exponentials (with the right base) are inverse functions of each other. That is $10^{\log(x)}=x$, $\ln(e^{x})=x$.
  • Exponential models: $y=a b^t$, or $y=a(1+r)^t$. From two points that are related by an exponential model, be able to find the initial value $a$ and the base $b$, or initial value and rate of increase or decrease $r$.
  • Be able to go back and forth from a doubling-time to a rate of increase or an exponential base. Be able to go back and forth from a half-life to a rate of decrease or an exponential base.
  • Be able to sketch graphs of $\log$ functions or exponentials. Know something about finding y- or x-intercepts of these, and their limits, domains, and ranges.
  • Shifts, stretches, reflections: Know how the simple transformations $kf(x)$, $f(x-k)$, $f(x)+k$, $f(-x)$, etc, are related graphically to $f(x)$. (There are more simple transformations than what I've listed here.)
  • Know how more complicated transformations--for example $g(x)=-3*f(x-2)$--can be related to $f(x)$ as a series of simple transformations, and how to evaluate a complicated $g(x)$ if you have a graph, formula, or table of values for for $f(x)$.
  • Be able to translate a written description of a problem into an appropriate model, or into some transformation of a model, and vice-versa.