Math Review Sheet for Exam 3
This exam covers Sections 3.1, 3.2, 3.4, 3.6 and 3.7.
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
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).