Section 5.1 - Vertical and Horizontal Shifts

I just finished section 5.1 in the Math Center and I thought it went pretty well. The only thing I'm still trying to grasp of horizontal shift (that to move to the right you have to say f(x-2) and to the left you write f(x+2) because the example on page 183 and 184, it's shifted to the left for 2 hours (f(x+2)) because it's saying that the new function is what the old function is what the old function was 2 hours after (+2) because it's moved to the left.. if that makes any sense!

Now that I'm done with all the homework (I wrote that before I did the homework and after I read the section) I understand it a lot more which is good because the second exam is on Friday! I think it's from section 2.5 to 5.1.

Oh, and I got 50/50 on my quiz that was last Wednesday and we got back today! And I need to get graph paper for my homework because we're drawing more graphs for homework right now so it's easier to do that with graph paper.

So, to get ready for the exam I'm going to do both the practice exams (which I got from the library today and copied) and go to my teacher's office hours tomorrow sometime from 11AM-noon so I can go over anything that I don't understand. From this past section (5.1) I'm going to ask my teacher about #19 which I didn't understand at all and of course, there was no answer in the book because it was an 'explain your answer' question.

For Monday I have to do sections 5.2 and 5.3 which are about reflections and symmetry (5.2) and vertical stretches and compressions (5.3) but I'm going to do those on the weekend so I can get ready for the exam on Friday.

Okay, I think that's it so I'll definitely update again before Monday.

Section 4.4 - log scales

I just finished section 4.4 which is about log scales. I have never ever in my whole life seen log scales and I've been very confused trying to understand the concept of how something isn't a linear scale but a log scale! But I did successfully finish the assigned homework problems for this section and I'm starting to understand what it actually means.. I think the part that's really hard for me is that I need to look at these scales in a whole different way. I'm used to looking at them with the thought that one inch always equals 5 units or whatever. Now, I have to think of it as one inch always equals 1 power (or exponent) of 10! And that means that if you translate 10^0 into 1 and 10^1 into 10 and 10^1.2 into whatever.. then it doesn't LOOK equal in a linear way... but it is in a log way! Ugh.. well I'm going to let this sit in my head for awhile and then look at it again.

I have to do 5.1 for Wednesday and I have my second exam on Friday. The exam is optional but ummm who wouldn't want to be able to get more credit!? I'm definitely taking both optional exams.. and since for some weird reason I'm doing better on my exams than my quizzes, it'll help a lot too.

So I don't have class today since it's President Day Weekend holiday.. but I did have class on Wednesday. Wednesday we had a quiz on sections 4.1, 4.2, and 4.3. The quiz was okay, but I ended up checking the first problem incorrectly so I said it had no solution when really it did. Fortunately, the solution I found was correct and I worked it all out on the paper so maybe my teacher will give me some credit, I hope because I did it right! The homework that was due on Wednesday was 4.2 and 4.3. Chapter 4 is about logarithms which are a little confusing. The first and only time I can remember learning about logarithms is in Algebra 2 and it wasn't a main focus for the class.. I remember not really understanding them but it didn't really matter since it was just a little part of the class. I know understand logarithms a lot more but it's definitely a big concept to think about and understand. I notice that there are some kinds of concepts in math that totally change your thinking about what math is and what defines math. The learner can either sort of admit that math concept into his or her brain and try and change what they think math is.. or the person can get really utterly confused and have a really hard time understanding this new concept... I don't know if that makes much sense but I hope it makes some sense! The homework this weekend (due Wednesday since we don't have class Mon. either) is to do 4.4 and 5.1 I think.. I don't remember in detail what either of those topics are about but I'll find out.

A habit I'm going to try and start and keep is something to help me with my quiz taking for this class. My teacher always gives us two questions (from that week's homework) which usually have multiple steps involved in getting the answer. For most of the quizzes I haven't been able to finish both problems and have time to check them over. So, after every section of homework, I'm going to choose two problems that I think he'll ask and then try and complete both of them in 10 minutes (the time he allows us for a quiz) and see if I can get through both of them. Hopefully, that will help me!

Section 3.1

I finished most of the assigned homework problems for section 3.1 (intro to the family of exponential functions). The main points in this section are about the exponential formula: f(t)= ab^t, b>0.

What's really important in the equation is that 'a' is the initial value of Q (at t=0) and b, the base, is the GROWTH FACTOR (b>1 gives exponential growth and 0 'r' is the "decimal representation of the percent rate of change"... meaning that 'r' is the percent given in the problem if it says something like Tom's salary grew 20% per year. 20% (or .20) is 'r'. Then to figure out 'b' so you can figure out an equation, you need to plug in 'r' into (1+r) = b. so... 1+.2 = 1.2 = b... then plug that into the equation of the function and you have f(t)= a(1.2)^t! And 'a' is the initial value.. so let's say Tom's salary starts at $1,000/year, so then plug that into the equation as well and you have:

Q=f(t)=1000(1.2)^t (t is in years)

Even though I understood all of this, I had some trouble on questions: 25d and all of 31. I'll ask my teacher about those soon. But I get the overall feel of this section.

Now on to section 3.2: Comparing exponential and linear functions!

Finishing up chapter 2

I just finished the review for chapter 2 as well as the section on getting ready for chapter 3, which is about exponential functions. The getting ready section was about exponents and rules of exponents. The section was good review and I need to remember to look again at the page with all the rules (pg. 139). Now I can move onto chapter 3. There's section 3.1 which is an introduction to the family of exponential functions. Section 3.2 is about comparing exponential and linear functions. 3.3 is about the graphs of exponential functions. 3.4 is about continuous growht and the number 'e.' Then I should do the review of chapter 3 (if I ever get through all of it!).

I know I haven't been too good about writing summaries about class but I have another class right after so I don't really have time right after precalc class. But I'm going to try and jot some things do that I can write about later. Today I was going to ask my teacher about a specific problem from section 2.6 but he wasn't in his office so I went to the math center and wrote down my name to get help. I did get really good help from a woman working there. However, the problem is that she didn't know exactly how I was learning things so she explained it in a little different way than my teacher would. I eventually got what she was saying, which really helped in figuring out how I would figure out the problem. I notice that sometimes even if someone is trying to help me figure out a problem and they don't fully help me, it usually helps me figure out how to figure the problem out on my own, if that makes any sense. It's nice that I've been understanding precalc so far, I hope it stays like this, challenging but understandable.

Now, to start chapter 3!

Catching up with Homework

I've gotten totally behind in my math homework since I've been to two conferences in a row in just 2 weeks. In the future, I'm definitely going to not do two big things in the first month of a new quarter. But now, I'm catching up and things are making sense. I just finished section 2.4 homework. 2.4 is about inverse functions and overall, chapter 2 is about functions, quadratics, and concavity. The homework went pretty well, I only had a couple of questions which the solutions manual answered easily. The only number I don't know the answer to is #14, since it's an even problem. Just to focus on this one, it's about finding the inverse function of H=f(t)=(5/9)(t-32). H is temperature in Celsius and t is in Fahrenheit. Since I got #15 correct (asking to evaluate certain expressions, which included some inverse functions), I know I understood #14 correctly and got the answer right.

I already read and did the homework for section 2.5 (concavity) since I had a quiz on 2.1 through 3.1 last Friday (which I got a 47/50 on!). I'm just going to glance over 2.5 and see if anything weird pops out at me. If not, I'm going to move onto 2.6 which is about quadratic functions. OH! Wait, actually I already completed the homework for 2.6. I did the homework last Thursday to get ready for the quiz as well. Okay, so actually, I'll glance over 2.5 (concavity) and 2.6 (quadratic funtions) and then do the review exercises for all of chapter 2 since 2.6 is the last section. Then, I will read and do the homework for section 3.1. Chapter 3 is about exponential functions and section 3.1 is the introduction to the family of exponential functions. I'll see how it goes!

My idea

Okay, I came up with this idea to start a blog about my math class. This blog will mainly be for my own use but maybe it could end up getting comments from another classmate or my dad or brother responding to a question that I have. I'm going to summarize what happened in a class after class and also after I do homework. I've been having trouble keeping everything in my head and I also have an easier time remembering and learning things if I write (or type) them down. So, I'll see how it goes, and just to tell you again: this is a blog mainly for my own use so it may not make sense or be interesting to others. If I'm specifically asking a question for someone to answer, I'll try and make it as clear as possible.