Homework: Review Sheet for Exam 2 This exam covers Sections 3.1, 3.2, 3.4, 3.5, 3.6 and 3.7. In addition,
we covered Sections P.7 and 1.3 on WeBWork.
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 a). Know
how to graph a line , and find the x- intercept and y -intercept of a line
(See also Section 2.4). Know how to graph a piecewise function (see
Example 5 and 6 on page 227, and problems #38-50 on page 234).
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.
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 formula for a function, like
f(x) = x2, for example, and asked to modify the formula so that the
new graph looks like the old graph shifted and/or reflected in a given
way (see problems #11-18, 27-32 pages 255-256). 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). Use graph shifting
techniques, along with the graphs of standard functions given on page
232 to graph (see problems #33-48 page 257). Understand how the
domain and range of the function change when it is transformed by
shifting and reflecting (see problem (4) on the Transforming Graphs
Hand Graded Homework).
From Section 3.5 Given a quadratic polynomial, be able to complete
the square to write it in standard form (see page 269). Be able graph a parabola from its standard form (by transforming the graph of x2) (see
page 267 #19-28). Be able to use the quadratic formula to find the zeros
of a quadratic function (find the zeros of function f(x) = ax2 +bx+c,
by setting it equal to zero and solving for x ) (see Section 1.3). Know
the vocabulary: vertex , maximum, minimum and zeros, and be able to
find these from the formula and identify these on a graph (see problems
#28-40 on page 266).
From Section 3.6 Know how to compose two given functions (i.e.
find f o 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).
Word problems involving quadratics Given a formula that models
the position of an object as a function of time, be able to answer
questions about times at which the object reaches given locations, and
the locations at which the object resides at given times . See #37 and
38 on page 268, Example 6 and 7 page 103, 1-4, and Problems #87,
88, 89, 90 page 1-7.
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