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# Math Review Sheet for Exam 3

This exam covers Sections 3.1, 3.2, 3.4, 3.6 and 3.7.

Topics:
From Section 3.1:
Know how to evaluate a function at a given number
(for example given a formula for f (x), be able to find f(5) (by
plugging 5 in for x)) (see problems #25-34 in Section 3.1). In particular,
be able to evaluate piecewise functions (see Example 3 on page
217, and problems #21-24 on page 221). Know what the domain of a
function is and how to determine it from the formula.

From Section 3.2: Know how to get information off of a graph,
including the domain and range of the function and its values (for
example, given the graph, be able to find f (a) for a given number a).
Understand the vertical line test, and be able to use it to determine
whether or not a given graph is the graph of a function. Be able to
draw the graphs of x2, x3, and 1/x, without spending a lot of
time plotting values (I suggest you memorize the shapes, the domains
and the ranges). See the table of graphs on page 232.

From Section 3.4: Know how to modify a formula in order to transform
the graph by shifting up, down, left or right or by reflecting across
the x- or y-axes. You will be given a modification of a formula and
asked how it changes the graph (see problems #1-10 page 255, and
#18,19 page 256). You will be given a graph of a function and asked
to draw the graph of a modified version of that function (see problems
#19,20 page 257). You will be asked to graph a given function using
graph shifting techniques, along with the graphs of x2, x3, and 1/x (see problems #33-48 page 257). Understand how the domain
and range of the function change when it is transformed by shifting
and reflecting.

From Section 3.6 Know how to compose two given functions (i.e.
find f ±g), given formulas for f and g (see Problems #29-44 page 276).
Know how to evaluate the composition of two functions given their
graphs (see Problems #23-28 page 276).

From Section 3.7 Know how to use the horizontal line test in order
to determine whether or not a given function has an inverse on its given
domain (see Example 2 page 281 and Problems #1-6 page 286). Be
able to find the inverse of a function (Example 6,7 and 8 page 283, and
Problems 31-50), and verify if a pair of given functions are inverses
(see Example 5 page 283 and Problems #21-30, page 286). Know how
to graph the inverse of a function given the graph of the function (see
Problems #65,66, page 287).