MAT1375 Precalculus FA2018

Topics:

• Sketching a complete graph of a polynomial
• Rational Functions and their graphs
• Solving polynomial inequalities using the same method we used to solve absolute value inequalities – see Section 1.4

A complete graph of a polynomial must show all of the important features of the graph:

• The x-intercepts (real roots) if any, and the y-intercept. Note that the y-intercept of a polynomial is the constant term.
• The turning points (local maxima or minima) of the graph, if there are any.
• The end behavior.

Here is the summary of graphing rational functions that I showed in class: it includes a worked example

MAT1375GraphRationalFnsNew

Solving polynomial (and rational) inequalities:

We use the same method we have previously used to solve absolute value inequalities, that is:

First solve the corresponding equation

Then investigate the intervals to see if they solve the inequality or not

Then look at the endpoints

The only difference is that now we will make use of our knowledge of the graphs of polynomials (and later, rational functions) to investigate the intervals. This is equivalent to the “test point” method.

Homework:

• Review the examples discussed in class. Make especially sure that you understand how we are using the graphs to solve the polynomial inequalities in Ex. 12.2(a,b)

Test 2 is scheduled for the first 50 minutes or so of class on Wednesday 31 October. Monday 5 November

Please make sure to review my course policies at this time.

There is a Test 2 Review assignment on WeBWorK.

This assignment is absolutely due at the stated time, and there will be no extensions. You will be able to view the solutions once the assignment has closed.

Also use the following Quizzes to test yourself: they contain material that is not included in the WeBWorK

MAT1375QuizPolynomialDivisionRemainderTheorem

MAT1375QuizPolynomialDivisionRemainderTheorem-solutions

MAT1375QuizRoundTripTheorem&OneToOne

MAT1375QuizRoundTripTheorem&OneToOne-solutions

MAT1375QuizPolynomialRoots

Other resources:

Here is a pretty good video: PatrickJMT on the Rational Roots theorem

The Wikipedia article on Rational Roots is also good and uses synthetic division

Please make use of the Piazza discussion board if you find any typos in these or if you need to discuss!

Topics:

• More on inverse functions: The “Round-Trip” Theorem (Observation 7.9 on p. 92 in the textbook, and also see Example 7.10 which follows)

• Long Division of polynomials.

This is section 8.1 in the textbook, and the WeBWorK also contains useful explanations of the steps involved. Don’t forget DMSB!

In the future applications we will be mainly interested in the remainder – I have hinted why this is so; it has to do with factoring, for one thing. We never say that there is no remainder, we say that the remainder is 0 (if that is the case).

Vocabulary to know:

dividend

divisor

quotient

remainder

Homework:

• Make sure that you have activated your Piazza account! If you are not sure how to do this, email me!

• This would also be a good moment to review my course policies and WeBWorK policies.

• Do the WeBWorK  assignments, due by Sunday midnight, but don’t wait to the last minute! I have reopened the assignment on iInverse Functions.

• Also do and check (per my Course Policies) the following problems from the textbook. You may put one of these on the board at or before the start of class (Just do it, don’t wait, but also don’t duplicate another student’s problem) as part of your 10 problems:

Exercise 7.4 p. 96

Exercise 8.4 p. 111, parts g and h

• Next time I will show you synthetic division, which is a quick way to do certain types of long division (like the ones we have done). I have a slideshow I will use, and you can see it here if you like:

MAT1375-LongDivisionSyntheticDivision-slideshow

Remember that if you get stuck on any of the problems or have a question about any of the material, you can post a question to the Piazza discussion board.

Here are solutions to Test 1, depending on which version you got:

MAT1375Test1AanswersFall2018

MAT1375Test1BanswersFall2018

(after Test 1)

TO BE UPDATED!!!

Topic: Inverse Functions

link to Cool Math source

Test 1 is rescheduled for Monday 15 October.

Test 1 is scheduled for the first 50 minutes of class on Monday 15 October (CORRECTION!!!).

Please make sure to review my course policies at this time.

Test 1 Review Self-Tests are here:

MAT1375Test1ReviewFall2018

The answers and some partial solutions, along with reference to WeBWorK problems (which usually have detailed explanations and solutions) for most of them:

MAT1375Test1ReviewAnswersFall2018

Please make use of the Piazza discussion board if you find any typos in these or if you need to discuss!

Due to unforeseen complications, the posts for yesterday’s class and for the Test 1 review are delayed. I expect to be able to post them this evening sometime. In the meantime, make sure that you check last time’s post and also look at the new WeBWorK assignments.

Topics:

• Lines, slopes, and intercepts (section 2.1 in the textbook)
• Introduction to the TI-84 (Session 4 in the textbook)

Here are some outline notes about the skills you need on the calculator:

MAT1375GraphingCalculatorBasicsNew

MAT1375GraphingCalculatorSolvingNew

Homework:

• Practice using your calculator by working through the examples in the textbook and in the above linked notes.

• There is no WeBWorK for these two topics, so be sure to do the following from the textbook:

Session 2, Exercises 2.1(a-c) and 2.3(a-c) – you may work one of these on the board at the start of class Wednesday if you like.

Session 4, Exercises 4.1, 4.2(a), 4.3(c-i), 4.6

Make sure that you know how to use the “Zero”, “Max”, and “min” functions on the calculator!

Topics:

• Some problems from the textbook on finding domains of functions defined by formulas: Exercise 3.6(a-d and f)

• Another example of a difference quotient: Example 3.3(b)

• Functions which are defined by graphs: Session 3 Examples 3.6-3.9 and 3.12

It is extremely important that you understand how to read graphs and how to identify the input and output values. Study these examples!

Homework:

• Study the examples discussed in class: make sure that you understand the notation and vocabulary that is being used.

• Make sure that you have signed into WeBWorK (and do the assignments) and that you have joined the Piazza discussion group. I am directing Piazza to re-send the invitation to those students who have not yet activated their Piazza accounts.

• You may join OpenLab and join this course on OpenLab if you wish. It is not required: you can read this blog without joining. But membership has its benefits!

• In addition to the WeBWorK, do the following problems from the textbook:

Session 2, Exercise 2.5(d, e) and 2.8

Session 3, Exercise 3.7

• Make sure to bring your graphing calculator to the next class and every class from now on. We will  be learning how to use it in these coming lessons.