Homework for the night of (due the following class day):
Thurs Jan 19 Read Sec 1.1-1.3; do Comprehension Checks throughout the reading.
Do all problems for Secs. 1.1-1.3, pp 32-33 End behavior, roots and multiplicity of roots to graph a polynomial
Rational root theorem example Fri Jan 20 Read Sec 1.4; do all problems p 33 Sec 1.4
Study for quiz tomorrow (Tuesday) on Section 1.1-1.4.
Read Sec 1.5; do exercises pp 33-34 #1, 2, 3 a-i
Tues Jan 24 Read Sec 1.6. Have ready HW questions you didn't understand ready on Sec 1.5
Do Sec 1.6 problems,do all exercises p 34
Read Sec. 3.1. Look esp at the domain examples and comprehension checks.
Fri-Sun Jan 27-29 The first test is Tuesday February 7
Ch 3 is essential to your understanding of all of mathematics. It addresses functions. Besides reading Ch 3 throughout the coming week, view these videos. Don't wait til before the first test to watch these.
Do pp 84-85 Sec 3.1 #1 a, c, d, f, #4 all #6 a b #7, #9
Read Sec 3.2
Mon Jan 30 Do p 85 #2, 3 b d, 4, 6 a b, 7
Tues Jan 31 Read Sec 3.2
Do problems p 85 #2, 3 b d, 4, 6 a b, 7
Short quiz tomorrow (Thurs) on solving equations and on functions (including definition of a function).
Thurs Feb 2 Do p 86 Sec 3.3 #1 a, b, c, d, 2 all, 4, 5 a b, 7
Read Sec 3.4.
Do Sec 3.4 pp 86-87 #1-5
EXTRA PRACTICE ON FUNCTION FEATURES
Fri-Sun Feb 3-5 Be prepared to ask questions on Monday on any topic you don't understand, any HW problem or video item. The test on Tuesday is on Ch 1 and Ch 3.
SKILLS FOR TEST 1
Simplifying exponential and radical expressions with numbers and variables
Rationalizing a denominator.
Factoring: common factors, reverse FOIL (including magic factoring), special products, grouping
Simplifying rational expressions (entails factoring skills) and state the restrictions on x
Adding, subtracting rational expressions (entails finding LCD)
Multiplying, dividing rational expressions (entails cancelling)
Solving equations: quadratic (with an x squared term, but not using the quadratic formula—either factoring and taking a square root) radical equations (squaring both sides, sometimes twice, then checking solutions in the original); rational equations (getting a common denominator and setting = zero, then factoring, etc. and check that answer is in the domain).
Functions: definition, domain, notation, operations on functions and the effect on domain of combining functions, esp composition
Showing a function is odd, even or neither by the definitions of these concepts
Showing a function is one-to-one by the definition of the concept
Finding the inverse of a function
Knowing when a function has an inverse
Facts about domain and range of a function and its inverse (they trade places), which leads to the fact that the composition of a function with its inverse gives x.
Reading and interpreting piecewise functions.
Tues-Wed Feb 7-8 Read Sec 4.1
Thurs Feb 9 Do Sec 4.1 pp 110-111 #1, 4, 6, 7, 8 This assignment will be collected on Friday.
Read Sec 4.2 and view the videos:
Fri Feb 10 Do pp 111-112 #1 a through o (these are the basic functions shifted left or right, up or down, flipped of x-axis or y-axis, stretched or compressed).
Read Sec 4.2 and view the videos from Thursday again.
Mon Feb 13 NEW: See your email and have questions for me based on what it addresses.
Do corrections on pp 3 and 4 of the test (to hand in).
Refer to Sec 4.1 and 4.2 essential diagrams of basic functions and transformations, noticing the domains and ranges of each.
View more transformations videos (see complete set on video page).
Continue with Sec 4.2 pp 111-112 #2, 5, 6
Tues-Wed Feb 14-15 Understanding important features of polynomials in order to graph them
Fri Feb 17
Sec 5.2 Equation of a line (point slope, slope-intercept); slopes of parallel and perpendicular lines; distance and midpoint). Work on this section over the weekend. We will review it after 5.1 and 5.3 are done.
Do pp 151-152 #3, 4, 5, 6, 8 a b e, 9, 10, 11 a b, 12 a c, 16, 17, 18
If you haven't watched them yet, view these short videos:
Do the problems pp 150-151 #1-9. Solutions are already posted; check your understanding against them.
Remember, the number of solutions goes to the way the parabola crosses the x-axis:
Discriminant = 0 means parabola touches x-axis once = 1 root
Discriminant < 0 means parabola doesn't intersect x-axis = no roots
Discriminant > 0 means parabola intersects x-axis twic = 2 roots
Do p 153 #1, 2, 3, 4, 8, 9, 10
Mon Feb 20 Keep working on the Sec 5.2 problems on lines. If you have questions, jot them down to ask in class:
pp 151-152 #3, 4, 5, 6, 8 a b e, 9, 10, 11 a b, 12 a c, 16, 17, 18
Continue working on problems Sec 5.1 pp 150-151 #1-9. Solutions are already posted; check your understanding against them.
Tues-Wed Feb 21-22 Read Sec 6.1 and 6.2
View Slant asymptotes
Do p 188 Sec 6.1, #2 all, #3
Sec 6.2 p 189 #3 a-d, 5 a b, 6 all
Thurs Feb 23 Read Sec 6.3 and 6.4
Do Sec 6.3 p 190 #1 a b c d e
Sec 6.4 pp 190-191 #1 a c d g, #3
Complete the Ch 6 rational function handout.
Be able to identify all features of a rational function: y-intercept, roots, VA, HA, and SA, and holes, if any, naming each item correctly. Asymptotes to be given in equation form.
Fri-Mon Feb 23-27 To help you study, here are the keys to all the handouts and take-home quiz:
And here is a list of problems to focus on for Exam 2. Please have questions to ask on Monday:
Study each parent function as graphed throughout your text.
Comprehension Check 4.1.
Examples 4.2.2 to 4.2.6.
p 11 problems #1 c, e, h, i, k, l, n, o
5.1: Study Examples 5.1.7, 5.1.8 and 5.1.9 (like the quiz).
pp 150-151 problems #2 a, b, d, e #3 a, b #4, 5, 6, 7, #8 c, #9 a, c, e, f
5.2: Study all Comprehension Checks and Examples, as well as Important Ideas 5.2.1, 5.2.2 and 5.2.4
pp 151-152 #3, 4, 8 b, e, and in the following, do several parts of each of #9, #10, #11; also #16-18
5.3: Know how to solve a quadratic equation (i.e., find the roots)
p 153 #1 b, 2a, b, d, e, 3 b, c, d, e, 4 a-f, 6 a-d
Ch 6 Look at all the graphed examples in this chapter. See the Videos link for a section on rational function graphing.
6.1: p. 188 #2 b, c, e, f, 3 a, b
6.2: p 189 #3 a, c, f, 5 a, 6 a, c, d, e
6.3: p 191 #1 a, b, c, d
6.4: p 191 #1 b, d, g, h