Daily Objectives

Section 3.2

Determine whether a graph represents a function.
Read function values and domain and range from a graph.
Graph basic functions by hand, including when combined as a piecewise function.

Section 3.3

Read coordinates of turning points, maximum and minimum output values, and intervals of increase and decrease from a graph.
State the definition of average rate of change.
Compute average rates of change (including velocity) from a graph, formula, or table using difference quotients.

Section 3.4

Describe in words the translation and/or reflections that should be applied to the graph of y=f(x) to obtain the graph for y=f(x+c), f(x-c), f(x)+c, f(x)-c, f(-x), or -f(x).
Sketch a graph of a function of the form y=f(x+c), f(x-c), f(x)+c, f(x)-c, f(-x), or -f(x) if given a formula or graph of the function f.
Recognize a formula as being of the form y=f(x+c), f(x-c), f(x)+c, f(x)-c, f(-x), or -f(x) for some basic function f.
Do the above when the formula or graph involves more than one transformation including when order of the transformations matters.
(Given a graph of y=f(x) and translations and/or reflections of it, be able to give the formulas for the functions with the resulting graphs.)

Section 3.5

Form f+g, f-g, fg, f/g, and find domains of these functions if given f and g.
Compose functions using formulas, graphs, tables.
Find the domain of a composite function.
Write a given function as a composition of other functions.

Section 3.6

State and use the definition of inverse function.
Find the inverse of f when f is given by a formula, graph, or table.
Use the definition of a one-to-one function to determine whether a function has an inverse.
Determine whether a function is one-to-one using the horizontal line test.

Section 4.1

State and use the definition of a linear function.
Construct linear functions if you know two points or one point and the slope, including in applications.
Use linear functions to make predictions and compute percentage error.

Section 4.2

State and use the definition of a quadratic function.
Complete the square to rewrite ax^2+bx+c as a(x-h)^2+k.
Find and use features of the graph of a quadratic function (vertex, axis of symmetry, maximum and minimum values, intercepts) from the formula and/or graph of the function.

Section 4.4

Define a function from a description of related quantities in words.

Section 4.5

Find, by completing the square or using the vertex formula, the maximum or minimum value of a key quantity or the input value that gives that maximum or minimum when the key quantity is given by a quadratic expression (or closely related expression).

Section 4.6

Determine whether a formula or a graph is a polynomial.
Identify the degree and leading coefficient of a polynomial.
Use the degree and leading coefficient of a polynomial to determine the overall behavior and the maximum number of turning points on its graph.
Sketch the graph of a polynomial obtained by shifting, reflecting, and stretching a power function.
Find the x- and y-intercepts of a polynomial.
Use the factored form of a polynomial to determine the shape of the graph near an x-intercept.
Find the intercepts, determine the behavior near intercepts, and sketch a graph of the polynomial (using excluded regions) if given a polynomial in factored form or that is easily factored.

Section 4.7

Use the definitions of rational functions and asymptotes.
Graph basic rational functions and their translations and/or reflections.
Find the domain, range, intercepts, and asymptotes of a rational function.
Use properties of a rational function and long division to sketch its graph by hand and check on a calculator.

Section 5.1

State and use the definition of an exponential function and distinguish an exponential function from a power function.
State and use basic exponent properties.
Describe properties of graphs of exponential functions given by formula, including domain, range, intercepts, asymptotes, and whether they are increasing or decreasing.
Graph exponential functions and their transformations using the properties.
Solve basic exponential equations algebraically and from a graph.

Section 5.2

State and use properties of graphs of exponential functions, including base e.
Graph f(x)=e^x and its translations and reflections.
Estimate values involving e.
Know how e and e^x arise in applications.

Section 5.3

State and use the definition of logarithmic functions.
Evaluate simple logarithmic expressions.
Convert equations from exponential form to logarithmic form and vice versa.
Use logarithms in applications to Richter magnitudes and decibels.
Graph basic logarithmic functions and their shifts and reflections and state their properties.

Section 5.4

State properties of logarithms and know why they are true.
Use properties of logarithms to manipulate logarithmic expressions.
Use the change of base formula to enter logarithms with other bases into a calculator.

Section 5.5

Be able to solve equations and inequalitites involving exponential and logarithmic expressions.
Remember to ALWAYS CHECK solutions.

Section 5.6

State formulas for compound interest and understand why they are true.
Use formulas for compound interest to compute account balances, time, or rates.
Find the effective interest rate given a nominal rate and vice versa.
State and use the doubling time formula and rule of 70.

Section 5.7

Use the formula for exponential growth to find the relative growth rate (or growth constant), predict populations, and calculate times.
Use the formula for exponential decay to find the decay rate, predict amounts, and calculate half-life or other times.

Section 12.1

State and use the definition of i and complex numbers and know why they are needed.
Perform arithmetic with imaginary and complex numbers and their conjugates.
Find conjugate pairs of roots of quadratic polynomials using the quadratic formula.

Section 12.2

Divide one polynomial by another using long division.
Use the division algorithm and to write a division in the form p(x)=d(x)q(x)+R(x) where R(x)=0 or the degree of R(x) is less than the degree of d(x).
Use synthetic division when dividing by a linear polynomial.

Section 12.3

Verify roots and provide their multiplicities.
Use the Remainder Theorem to evaluate a polynomial and check if a given x-r is a factor.
Use the Factor Theorem to find remaining roots of a polynomial when one or more is given.
Construct a polynomial with given roots and multiplicities, and possibly also with additional conditions on degree or coefficients.

Section 12.4

Know what the Fundamental Theorem of Algebra and its consequences say and when they apply.
Apply the Fundamental Theorem of Algebra to factoring and finding roots of polynomials.
Express a polynomial in factored form.
Construct a polynomial from its roots and possibly other conditions.

Section 12.6

Know the Conjugate Roots Theorem.
Given one or more real or complex roots, find remaining roots of a polynomial and its factored form.

Previous Announcements

Review sections in Chapters 1 and 2 as needed - I will assume you know this material.
Please put homework in a single column on the paper and leave enough blank space for comments and marks from the grader.
Use the class directory to form study groups. As long as you make an honest effort to try the problems on your own first and write up solutions individually this can be a productive and fun way to study.
From now on no late homework will be accepted and no make-up quizzes will be given out of fairness to your colleagues and to avoid causing an excessive amount of extra work for the grader and me. However, your lowest homework and quiz score for the semester will each be dropped in calculating your grade.
Please use graph paper for all graphs on homework. Always mark scales on axes and draw graphs large and carefully.
Please use = when you mean exactly equal and the approximate symbol when you round to get an approximate answer. Provide an exact answer unless asked to provide an approximation.
Always show all work and intermediate steps by hand and then check work on your calculator whenever possible.
Learning how to fix mistakes on returned homework and quizzes is a good way to start studying for exams. Working additional problems, for example from the review or test at the end of the chapter, without the book available is also useful. Use the list of objectives on this page as a checklist of things you should be able to do. A sample exam with instructions on how to use it most effectively is linked on the course web page.
Without dramatic changes in the amount or quality of the time spent studying for this class and/or the amount of help you receive from me and/or the Math Center, you should not expect your scores on later exams to change dramatically from your score on a previous exam. You should be averaging 6-9 hours of productive study time per week on this course. Links to many learning and math study strategies are available on my Useful Links page: http://www.isu.edu/~krilcath/links.html.
Make sure you figure out how to work any parts of Exam 1 you did not solve correctly.
The slip attached to your exam records all scores earned to date - please check that all homework and quiz scores are properly recorded. The revised Exam 1 score was found by adding 25% of points earned by reworking exam problems (do not expect this to occur on future exams). Your estimated grade is found by weighting your homework average as 8%, quiz average as 8% (without dropping a low homework and quiz score since there are so few so far), and revised Exam 1 as 84% since it is the only exam score so far.
Solutions to quizzes, class problems, and Exam 1 are available from me for borrowing or photocopying.
The homework and calendar web pages have been revised to have consistent due dates.
Remember that solutions to previous exams and quizzes are always available from me for photocopying.

Previous Announcements

Always do all parts asked for and remember to record on paper what you did on your calculator so we can tell what you did.
Your lowest homework and lowest quiz score will be dropped, so no late homework and no make-up quizzes.
There is review of rounding, exponents, roots, and factoring in Appendices A and B at the end of the text.
If you miss class, you may bring homework to my office, PS 316C, or the Math Office, PS 318, or scan and e-mail it to me, or fax it with my name on it to the number on the syllabus. In all cases you should e-mail me and/or call me to make sure I know you submitted it so it does get to the grader.
Remember, late homework will not be accepted and no make-up quizzes will be given since one low homework score is being dropped.
We are skipping 12.5 and the last part of 12.6 on Descartes's Rule of Signs.

Exams
Use the list of objectives on this page to guide your studying for the exam. The best way to study is to work lots of extra problems, especially on those objectives you are weakest on, and to do so without looking at the book or your notes for hints.
Sample previous exams are available from the course web page.
They do not guarantee anything about the questions that will appear on the actual exam. The sample will be most useful to you if used like a real exam and taken in 55 minutes with no books or notes available, then graded using the solutions available .
If you are not able to sit and correctly work a large percentage of the final in 2 hours with no books or notes available then you should not expect to be able to do well on the actual final.
Make sure you are practicing to be able to do math for 1.5-2 hours!
Make sure you know how to fix all errors on quizzes, old exams and homework. Remember that solutions are available for quizzes and exams.