Review Chapter 1 and make sure you are on top of the techniques covered in that chapter.

2.1 Understand the "four ways to represent a function" (p.137):
Algebraic, Visual, Verbal, Numeric.
Be able to convert the expression of a function from one "way"
to another. (Verbal <--> Algebraic: *Exercises 3 and 7*;
Algebraic --> Numeric: *Exercise 11*; Visual <--> Verbal
*Exercises 61 and 68*).

2.2 This section treats Algebraic <--> Visual and Numerical -->
Visual to some extent. Understand the concepts *domain* and *range*
and where the domain and the range of `f`
appear in the graph of `f` (*Example 7 p.161, Exercises 1,2*).
Know some examples of non-polynomial functions
(absolute value *Example 3 p.158*; step functions like the
"greatest integer" function *Example 4 p.158*).
More generally, understand piecewise-defined functions (*Example
2 p.157 Exercises 63,67*) and their graphs. Understand the
"vertical line test" (p.161) which tells which curves can be
the graph of a function (*Exercises 5,7*).

2.3 This section has some important examples of functions that turn
up everywhere. Understand "`d` is proportional to `t`"
(Example 1) and "`y` is inversely proportional to `x`"
(Example 2) as sentences representing the functions `d = kt`
and `y = k/x` respectively. Be able to calculate `k`
from data (*Exercises 23, 26*).

2.4 Understand "average rate of change for the function `y = f(x)`
between `x = a` and `x = b`"
(*Box p.175*). Be able to calculate it in examples:
from formula for
`f(x)`(*Example 1, Exercise 3*),
from table (*Example 3, Exercise 20*),
from graph (*Exercise 15*).
Understand the concept "`f` is increasing
on an interval `I`" (*Box p.180*), and "decreasing". Be able
to use a graph to find intervals on which `f` increases or
decreases (*Example 5 p.180, Exercises 23-26*).

2.5 Understand how the graphs of `f(x+a), f(x)+a, f(cx), cf(x)`
are geometrically related to the graph of `f(x)`, for `a`
positive and negative, and for positive `c` greater or less than one.
(*Examples 1,2,3,4,7; Exercises 1,3*). Understand how the graphs of
`f(-x), -f(x)` are geometrically related to the graph of
`f(x)` (*Example 5, Box p.188*)

2.8 Understand how to combine functions arithmetically (`f+g, f-g,
fg, f/g`) and how to figure out the *domain* of a combination.
*Examples 1,2; Exercises 3,5*. Understand the operation of
composition in terms of the "machine" representation (Figure 3).
Be able to work out the composition when both functions are given
by graphs *Exercises 23,24*.

2.9
Be able to
apply the "horizontal line test" to the graph of `f` to
see if `f` has an inverse (Figures 3,4,5). Understand
how *restriction of domain* can change a function to
one which satisfies the horizontal line test (Figures 4,5).
*Exercises 62,64*.
Be able to calculate the inverse of a function given by
a formula (*Box, p.233; Exercises 31,38*).
Understand that if `g` is the
inverse of `f`, then the graph of `y=g(x)` and the
graph of `y=f(x)` are related by reflection through the
diagonal `y=x` (Figures 8,9,10) *Exercises 52,54*.

Use the Chapter Review on pages 240-245 for further reviewing.

3.1 Understand the terminology "monomial" and "polynomial."
Understand that the large-scale behavior of a polynomial is
determined by its *leading term* (*Example 2*) and
that the end behavior has exactly four possibilities (*Box
on p.260*). Understand that a polynomial of degree `n`
can have AT MOST `n-1` bumps (local extrema)(*Example 7,
Exercises 37-42*).

3.2 Long division of polynomials. Understand the "Division Algorithm"
(*Box, p.273*) and be able to calculate quotient and remainder
in "polynomial long division" (*Example 1, Exercises 3,5*).

October 8 2003