Section 4.1: Exponential Functions

1. Evaluate an exponential function $f(x) = a^{x}$ at integer and rational values of $x$.
2. Specify the domain and range of an exponential function.
3. Determine whether a given function is an exponential function.
4. Sketch the graph of an exponential function $f(x) = a^{x}$, including its behavior as $x$ approaches both positive and negative infinity.
5. Given the graph of a function $f(x)$, sketch the graphs of $g(x) = f(x) + c$, $g(x) = f(x - c)$, $g(x) = -f(x)$, and $g(x) = f(-x)$.
6. Use (but do not memorize!) the formula for compound interest to find the amount of money in a savings account if the account starts with a principal $P$, has yearly interest rate $r$, and is compounded $n$ times per year for a total of $t$ years.

Section 4.2: The Natural Exponential Function

1. Give the decimal expansion of the number $e$ to 3 decimal places.
2. Sketch the graph of an exponential function $f(x) = e^{x}$, including its behavior as $x$ approaches both positive and negative infinity.