MAT1375 Precalculus FA2017

This is the schedule for the math specialist tutoring this semester:

Perkins 2017B

The schedule will also be posted on the Resources page on this website.

Test 1 is scheduled for the first hour or so of class on Wednesday 27 September. Please make sure that you have read the course policies on tests.

Review self-tests: MAT1375Test1ReviewFall2017

UPDATE: Answers and references with corrected answer to problem 5c in Self-Test 1:

MAT1375Test1ReviewAnswersFall2017

Also, linked below is the video I have previously linked showing the “Test point” method for solving an absolute value inequality (which is what we did in class and is done in Example 1.18 in the textbook): please note that you must use this method and no other method on Test 1, just as on the Quiz.

Here is a video showing the method (“Test point method”)

• Old business:  If you haven’t already seen this from PatrickJMT, a nice video on finding domain and range for a function defined by a graph.

Topics of today:

• More practice with the graphing calculator: changing the window size, zooming, making the window “square”.

• Finding the zeroes (x-intercepts of the graph) of a function using the “zero” function

I am having trouble uploading my handouts. I hope to fix this soon, but in the meantime I will post them on Piazza.

Also, here’s a video for finding zeroes of a function (or x-intercepts) using the “zero” function on TI-84plus

(What we did today, following the same steps as on the handout I gave you.)

Homework:

• Go through Session 4, with your graphing calculator in hand, and work all the examples through Ex. 4.6(b) along with the book. Make sure that you can do all the things described in the examples.

• Fill out the outline notes “Graphing calculator basics” based on what you did. Also fill out the two examples on the 2nd page (if you did not do so in class).

• There is no WeBWorK on these topics. Make sure that you do the exercises in the textbook, Exercises 4.1, 4.2 (a), 4.3 (c)-(i)

• The quiz on Monday will be on functions defined by formulas and functions defined by graphs, Session 3. Make sure that you have done the textbook exercises 3.1 (a)-(b), 3.2, 3.4 (a)-(f), 3.6 (a)-(f), 3.7 (a)-(g) and (m)-(t), 3.8, 3.9

• Don’t forget that Test 1 is scheduled for Wednesday 27 September, the first hour or so of class. Read the course policies on tests, please. Review self-tests and answers are in a separate post.

Don’t forget, if you get stuck on a problem, you can post a question on Piazza. Make sure to give your question a good subject line and tell us the problem itself – we need this information in order to answer your question. And please only put one problem per posted question!

Topics:

• Difference quotients: more practice (Exercise 3.4(a) and (f))

• Functions defined by a graph: reading off function values, find domain and range. (Examples 3.7  and 3.8, on handout)

• Introduction to graphing calculator (to be continued next time)

Homework:

• Review and study the examples we discussed in class (listed above). Make sure that you understand how we can find the domain and range of a function from its graph.

• Do the WeBWorK:  please do not wait to the last minute!

• Also do the following from the textbook:  Exercises 3.7 (a)-(g) and (m)-(t), 3.8, 3.9

These contain extra practice and also a few things that are not in the WeBWorK.

• Make sure that you bring your graphing calculator to class next time and every time from now on, so you get practice in using it. We will use it extensively next time.

I believe that I have corrected or fixed all of the links in the previous posts on this blog, but if you find a link in any post that is broken or leads to the wrong thing, please let me know!

Don’t forget, if you get stuck on a problem, you can post a question on Piazza. Make sure to give your question a good subject line and tell us the problem itself – we need this information in order to answer your question. And please only put one problem per posted question!

Here are the solutions to the first quiz:

MAT1375QuizIntevalsAbsoluteValueEquationsSolutions

Here are the solutions to the second quiz:

MAT1375QuizAbsoluteValueInequalitiesFunctionsSolutions

Please let us know if you find any typos or other errors in these!

Topics:

• More on functions defined by formulas:

Difference quotients (Example 3.3)

Finding domains of the four types of functions we have studied so far (Example 3.5)

I strongly recommend computing the difference quotients by breaking the process down into 3 steps, as I did in class (and as is done in our textbook):

First, find

Then find

Finally, find

Write down what it is that you are computing at each step, as I did (and as they do in the textbook) – this makes it easier to follow when you or someone else goes back to read your work.

When finding the domains of the four types of functions, it is important that you understand why we do what we do.

For a polynomial function, there is no problem substituting any real number into its formula, so the domain is the set of all real numbers .

For a radical function of even index like a square root function, the radicand cannot be negative, because for the time being we are insisting that the values of the function must be real numbers. So we need the radicand to be .

IMPORTANT: solve that inequality to find the domain. DO NOT SOLVE AN EQUATION AND THEN STICK AN INEQUALITY SIGN INTO THE RESULT! That will not always work, and you may forget the inequality sign!

For a rational function, we need the denominator not to be 0.

For a piecewise-defined function, the domain is the union of the pieces of domain where it is defined. Sometimes (not always) that union can be simplified.

Study the examples I discussed in class and make sure that you understand why we do what we do!

• New topic: lines and their slopes, and putting the equation of a line into slope-intercept form  (See Example 2.6 in the textbook)

It is most important that you develop an intuition for how the slopes affect the graphs. See the graphs with different slopes which are given on p. 15 in Section 2.1.

Homework:

• Last reminder: make sure that you have done everything that is listed on the first day post! Most especially, make sure that your City Tech email address is in the User Information in WeBWorK. There are still a number of student who have not done this, and it means that if you send me an email from inside of WeBWorK I will not be able to reply to your email.

• Review and study the examples we discussed in class (listed above). You may also want to refer to my slideshow MAT1375-FunctionsByFormulas-slideshow which I used last time.

• Do the WeBWorK: due by 11 PM tomorrow, Tuesday, and please do not wait to the last minute!

• Also do the following from the textbook:  Exercises 3.1 (a)-(b), 3.2, 3.4 (a)-(f), 3.6 (a)-(h)

These contain extra practice and also a few things that are not in the WeBWorK.

• Make sure that you bring your graphing calculator to class next time and every time from now on, so you get practice in using it. We will use it extensively next time.

• Tomorrow is primary election day in NY, so if you are a registered voter check out the NYC Campaign Finance Board’s Voter Guide and don’t forget to vote!

I believe that I have corrected or fixed all of the links in the previous posts on this blog, but if you find a link in any post that is broken or leads to the wrong thing, please let me know!

Don’t forget, if you get stuck on a problem, you can post a question on Piazza. Make sure to give your question a good subject line and tell us the problem itself – we need this information in order to answer your question. And please only put one problem per posted question!

Here is my slideshow on how to use Piazza to best effect: MAT1375:1575-UsingPiazza-slideshow

Apologies for the late post!

Topics:

• Functions defined by formulas and function notation

• Finding domains for four different types of functions (see the MAT1375-FunctionsByFormulas-slideshow)

• Finding a difference quotient step-by-step: see example 3.2(i-l)

Important:   is not the same thing as . This is a common source of errors!

means that you input everywhere in place of in the formula for f.

means that you take and add to the output.

These distinctions will be important when we discuss transformations of function later in the course, also!

Homework:

• Review finding the domains of the four types of functions we have discussed so far, and also finding the difference quotient.

• Do the WeBWorK: I have delayed the due date until Tuesday because of the lateness of this post.

• Also make sure that you have done everything listed in the first day post

and in the post from last time.

It is especially important that you make sure that your City Tech email address is entered in the User information in WeBWorK.

• There will be a quiz at the start of class next time. Be on time! It will be on solving absolute value inequalities by the test point method: see the post from last time for a video. It will also include problems like those from Section 2.2, on the concept of a function and function notation.

Don’t forget, if you get stuck on a problem, you can post a question on Piazza. Make sure to give your question a good subject line and tell us the problem itself – we need this information in order to answer your question.

Here is my slideshow on how to use Piazza to best effect: MAT1375:1575-UsingPiazza-slideshow

Topics:

• Solving absolute value inequalities – using the method of Example 1.18

Even if you happen to know another method for solving absolute value inequalities, you must learn and use this method, because we will build on it to solve other types of inequalities. Also, the other methods do not always work except in the very simple (linear) absolute value inequalities.

Here is a video showing the method (“Test point method”)

• Functions

The concept of a function

Functions as mappings

Domain and range of a function

Function notation

Homework:

• Make sure that you have done everything from the first day post.

• Review the method of solving absolute value inequalities in Example 1.18 (Test point method). Make sure that you understand what is being done at each step.  See the problem I have posted on Piazza for an absolute value inequality that cannot be solved by the other methods!

• Do the WeBWorK on absolute value equations and inequalities – due by Tuesday 11 PM, but don’t wait to the last minute!

• There is no WeBWorK on the Functions topic, so make sure to do and check the assigned problems from the textbook, Session 2 #2.5-2.8 all.

• For more practice on solving absolute value inequalities, do session 1 #1.7(a-f)

• There will be a quiz at the start of class next time. Be on time! It will be on interval and inequality notations, and solving absolute value equations.

• Monday is a holiday. Happy Labor Day! Next class is next Wednesday, the 6th of September.

Don’t forget, if you get stuck on a problem, you can post a question on Piazza. Make sure to give your question a good subject line and tell us the problem itself – we need this information in order to answer your question.

This website is your “one-stop shopping” for all matters related to our class. Please check for the post of the day every time we meet!

Here is the news from the first day:

You should have received a copy of my course policies with the instructions for WeBWorK on the other side.  If you were absent or loose them ever, they are available as pages here on this blog. (Follow the links.)

Our course textbook is available at this link.

Here are the topics of the day: to be updated when I have time. Quick run-through now.

• The Real number system and its ingredients.

• Geometric and algebraic definitions of absolute value.

• Solving absolute value equations.

• Intervals and inequalities. Three notations.

Homework:

• Find and deal with your City Tech email: you must use this email address in WeBWorK and to join the Piazza discussion board. Also, City Tech is already sending you emails here!

• WeBWorK has been set up for this course. The WeBWorK is here. (corrected link)

Please follow these instructions: MAT1375 WeBWorK information Fall 2017 in order to log in. After changing your password and entering your citytech email, you may start on the Orientation assignment to get used to how WeBWorK works.

A common problem that occurs when people try to log in using iPhone is that there is automatic capitalization for the first letter when you type in your username or password. Check to make sure the capitalization is turned off (or turn it off) while you type!

AFTER you’ve done at least 7-8 of the Orientation problems, you should start on the assignment which is due by tomorrow evening 11 PM. Don’t wait to the last minute!

• Join the Piazza discussion board for this course by following this link. You will need to enter your City Tech email in order to join. I will post extra credit questions here from time to time!

• Also don’t forget the extra practice problems from the textbook. See the Course Outline for Session 1, up to #1.6 only.

See you on Wednesday!