finalreview

# finalreview - Final Exam Checklist Math 111 College Algebra...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 P=Pg(1+—) Tl. 0 Formula for continuously compounded interest: P = P0671 0 Vertex of a parabola of the form f(:z:) a 0x2 + bx + c: in —_b 2a ’ 2a '_ —b:l: x/b2 + 4m: _ —9a 0 Quadratic formula: 13 d ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern