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.

Old Announcements

Time management worksheet and syllabus assignment:
- Read the course information/syllabus carefully, complete the time management worksheet, and on the back write responses to the following.
  - On the syllabus what did you find most interesting/surprising and what is most useful?
  - Name one thing you are passionate about (subject, topic, course, activity, sport, book, movie,...).

Late homework quickly gets out of hand and becomes a major inconvenience, requiring substantial extra time to grade separately and to keep track of. So to be as fair as possible to everyone and as stated in the syllabus, I will be dropping two lowest homework scores and two lowest quiz scores and will therefore collect no more late homework and give no make-up quizzes.
The class directory and some solutions are posted in Moodle. To login use your usual ISU username and password.