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Unformatted text preview: Final Exam Checklist Math 111: College Algebra December 3, 2008 This is a list of topics which I expect you to understand and solve problems about on
the final exam. I have bolded what I feel are the most important topics of the course, but
you will want to know all of the topics to do well 011 the exam. 0 O O Deﬁnition of a function and ways to represent functions. Determining if a graph represents a function. (Vertical line test) Function notation. Evaluating a function at a given value or expression.
Interval notation. Deﬁnition of domain and range of a function. Determining the domain of
a function. Finding maximum and minimum values of a function given a graph. Determining on What intervals a function is increasing, decreasing, concave
up, and concave clown given a graph. (Note: One of the main goals of calculus is
to determine this information given only the equation for a function.) Deﬁnition of average rate of change; total change. Units of average rate of change.
Deﬁnition of a linear function. (Constant rate of change.)
Deﬁnition of slope; slope-intercept form of a linear function. Recognizing linear growth or decay and solving word problems associated
with linear functions. Relationships between parallel and perpendicular lines.
Horizontal and vertical lines. Absolute value. '3!I!talk-i.-IIII:IitllIIat;an-a.anemia:Iﬂlrﬁilﬂiu-"umn-laéif-L ~~~~~~~ ' Rules of exponents; simplifying exponential expressions.
Relationship between radicals (f) and fractional exponents.
Converting numbers to and from scientiﬁc notation. Converting units of measure given appropriate conversion factors. 0 Deﬁnition of an exponential function. (Base 0. and base 6.)
0 When an exponential flmction represents growth or decay. 0 Deﬁnition of growth / decay factor, growth / decay rate, and continuous growth / decay
rate. 0 Recognizing exponential growth or decay and solving word problems associated with
exponential functions. 0 Converting between y = C's.t form and y = Ce“ form. 0 Constructing exponential functions to represent situations given the initial
value and other information (such as the growth / decay factor, growth / decay
rate, or continuous growth/ decay rate.) 0 Properties of the graphs of exponential growth and decay functions. 0 Deﬁnition of common logarithm and natural logarithm. 0 Properties of the graphs of logarithmic functions. 0 Inverse relationship between certain exponential functions and logarithmic functions.
0 Relationship between the graph of a function and the graph of its inverse function. 0 Rules for logarithms. (Including the inverse rules Whﬂo Kid, 42> “9‘1: x
0 Fully contracting or expanding a logarithmic expression. 0 Using logarithms to solve an equation where the variable is the in exponent
(an exponential equation). 0 Solving logarithmic equations. 0 Computing common logarithms and natural logarithms on a calculator. 0 Solving problems involving compounded or continuously compounded interest. 0 Finding the half—life of an exponential decay function. 0 Finding the doubling time of an exponential growth function. 0 Identifying the degree and leading coefﬁcient of a polynomial. o Identifﬁng the concavity, vertical intercept, and vertex of a quadratic function. 0 Solving a quadratic maximization or minimization problem by ﬁnding the vertex. 0 Factoring a quadratic polynomial. WW— 0 Solving a quadratic equation by factoring or using the quadratic formula. 0 Deﬁnition of a polynomial. Special names for polynomials of degree 0 through 5. 0 Maximum nmnber of turning points and horizontal intercepts for a polynomial of a
certain degree. 0 Factored form of a polynomial given zeros r1? . . . ,rn. Formulas to Memorize 0 Average rate of change of a function ﬂat") on an interval [m b]. flbl—ﬂal 2 main _ég_rise b—o xguélh Ar— run 0 Formula for compound interest: r at
Tl. 0 Formula for continuously compounded interest: P = P0671 0 Vertex of a parabola of the form f(:z:) a 0x2 + bx + c:
2a ’ 2a '_ —b:l: x/b2 + 4m:
_ —9a 0 Quadratic formula: 13 d ...
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- Fall '08