Additional info on transformation

     Hello class, This is nick who is about to show you how equations on trasnformation works and explain about this stuff. I hope i don't give you a cancer with my terrible grammar(also i don't find any multiply and devide signs on my lap top. i also have no idea how to put fractions in with this.) and let's don't waste more time on reading this and get in to it.


How Trasformation Equations work.



      Hopefully, you should see what i scanned from the booklets on how equations work.  As you see above, a and d affects the y-values and the effect on the graph is said to be the same on like b and c that affects oppsite. But explaining in words wouldn't help you so much with this terrible grammar -_- so i'll just explain this by a made up question.

 

     If f(x)=(-2,4), what ordered pair does the graph -2f(4(x+2))+4 produce?

 

     Well first, we need to know what the steps are, which is listed on the next page of booklet. 



The steps that you guys don't really need to know if you know the idea in my opinion, but never bad to know.

      using this example of steps above, we should multiply the y-value by -2 which makes it......



 -2*4=-8

 

     and now we need to add 4 and it makes......

-8+4=-4

 

     Now we know that our new y value is -4. Now, what about x-value?

    

     Unlike the y-value, all the thing you see is a TRAP! you should devide by 4 instead of multiplying it! which makes the x-value.......

 

-2/4=0.5

 

     and now we subtract this by 2 instead of adding it(btw you only devide or multiply x-value, not the one next to it.), which make it......

 

0.5-2=-1.5

 

     now there is our x-value, which makes our answer (-1.5,-4).

 

     See how it works??? See how Insides(a and d) affects the y-value and how outsides(b and d) affects the x-value?? Well now, we are going to have graphs to help you understand better in this one.



     The graph of a function f(x) is given below. On the same set of axes draw a graph of the function y=2f(x-1)

    

 

    The coordinates of f(x) are (-5,0),(-4,3),(-2,-3),(-1,2) and (2,0), now we should multiply the y-value by 2 and add 1 to our x-value. which makes these new coordinates......

 

(-5,0) to (-4,0)

(-4,3) to (-3,6)

(-2,-3) to (-1,-6)

(-1,2) to (0,4)

(2,0) to (3,0)

 

now if we draw this on the graph.......

 

 



     A new(ugly) line comes out.

 

     I think that should be enough explaining or giving enough cancer to you guys, I hope you get the idea well by watching this and now it's time for me to go.

 

     (P.S. But before i go i want to pick who's gonna be next and that will be number 1 or 10 if 1 is not availiable.)

 



Reflections and Stretches

Hello, my name is Kyle Cuellar. I will be summarizing our class on Reflections and Stretches. Mr. Piatek began the class by starting a new lesson (reflections) and by making us look at the graph below.

We then answered two questions about the graph.

 When you reflect a point over the x-axis, you will need to make the y-values negative and when you reflect a point over the y-axis, you will need to make the x-values negative.

After that, Mr. Piatek answered example 1. He also showed us the rules about reflections.

 Here are the examples that we answered during the class:

Reflection over x-axis

 Reflection over y-axis

 Reflection over x-axis but y-values are multiplied by -2

Reflection of f(x) over both x-axis and y-axis

The next day, Mr. Piatek started another lesson and it's all about stretches. There are two types of stretches, vertical stretches and horizontal stretches.

Mr. Piatek then showed us how to do the first example.

I found a video about the stretches and reflections of functions:

Just a quick note: When performing transformations always perform the horizontal and vertical stretches before the translations (up, down, left, right).

This is what we learned in class the last two days. I hope I was able to help you with this information.

Sorry I'm not a good writer. Thanks for reading this blog though. I look forward on learning with all of you this sem.

Your Classmate,

Kyle 

Introduction to Basic Transformations: Translations of Functions

Hello everyone! For those of you who don't know me, my name is Marynea Collina (or just Nea; however, I have been trying to convince everyone to call me using my full name because it sounds ambiguous.) I am the one sitting at the front who is either talking uncontrollably or on the verge of falling asleep. (Just kidding.)

But enough about me! Anyway, I am here to "attempt" to summarize what we've learned today. "Attempt" because I was doing the latter during Pre-Cal. Close to falling asleep, that is. (Just kidding. Don't hate me, Mr. P. The class is cool. Really. I promise. It really is.) In case you guys weren't paying attention, it was about Genetics. Well, in case you aren't paying attention again, I was only kidding. Today, what we REALLY talked about was the Translations of Functions, which marks the first lesson of the second unit.

Mr. Piatek introduced the unit with a recap of the lessons we covered back in Grade 11 (which I hope you remember still): functions, quadratics, graphing. As we all know, function is a relation which assigns exactly ONE element in this range for each element in its domain.

Just for the purpose of making myself and everyone else remember, here's a quick recap of it:
                            f(x) = y ---> it means that for every x value, there is only one y value.

One easy way to know if it's a function or not is to make a table of values. Another is to do a vertical line test. If it intersects the graph twice, then obviously it is not a function. Therefore, a circle cannot be a function.

y = x^2

The graph on the left side shows a parabola that can be considered a function; the lines should only intersect once.

You can also create a table of values:

• x	y
  -2 -1  0  1  2	4 1 0 1 4

You will be able to see that there's only one X for everything. There might be y-duplicates, but Xs continued to be unique (if that makes sense).



I won't explain any further because I know you guys know about it already. If you need help, just ask Mr. P anytime, or even me. (Do the latter if you want to fail.)

Now that you remember how to graph functions or what they really are at all, we are now able to shift the graph of functions.

He introduced a new topic (perhaps not so new to some people) which was Transformations. It is the moving, flipping, stretching, or compressing of the base graphs. It could either be: translation, reflection, or stretch. Unfortunately, we only got to Translations, which are the horizontal and vertical movements (shifts) using basic shape.

A few rules that it contains are:

1. Vertical Translations:  only y values are affected
    y = f(x) + k ------> shifts the entire graph up k units
   y = f(x) - k --------> shifts the entire graph down k units
2. Horizontal Translations: only x values are affected
   y = f(x-h) ---------> shifts the entire graph right h units
   y = f(x+h) --------> shifts the entire graph left h units

Remember! k values remains as is and h values must be read as opposite.
      example: f (x-4): h = +4

Here's an example from the booklet that we solved in class:

For b), it indicates a vertical translation, therefore not affecting the y-values, only x. f(x) + 3 asks for the x-values to be shifted upwards by 3 units (since it's positive 3 and a k-value, it ought to stay as is). So you add 3 values to the x-values:

0+3 = 3
1+3 = 4 ... etc.

Although for c), it is a horizontal translation, so x values change. f(x-3) contains an h-value, so we read it as an opposite value. -3 ---> add 3 units for y-value (to the right).

0+3 = 3
1+3 = 4
4+3 = 7 .. etc.

Oh well, I don't think I have anything else to say. It was the beginning of the unit and didn't really contain that much substance. Although, I bet this topic will play a big part for the remaining of this course. I'm half-asleep right now. Always will be. I hope I made any sense. If you seriously need any help still, don't be afraid to ask Mr. P or your peers. I am here to support as well! Don't forget to do your homework. xx

Yours Truly,
Marynea Collina ヾ(＾∇＾)

(P.S: Is anybody reading this at all? Let's make a petition to make Mr. P to change the background of our blog. Seriously. Am I the only one who cares about the background?)

Binomial Theorem

Hello classmates, I am Reedhee Modha and I will be summarizing about what was covered during our morning class today. Mr. Paitek started, the first class with the quiz and we all had the same question for the first time, lesson reviewing expanding and simplifying the binomial from yesterday's class. And later on he taught us about basic exponent rules, Pascal's triangle and binomial theorem. 

Expand binomials as follows:

(x+y)0=[1]

=1

(x+y)1=[1]x1y0+[1]x0y1

=x+y

(x+y)2=[1]x2y0+[2]x1y1+[1]x0y2

=x2+2xy+y2

(x+y)3=[1]x3y0+[3]x2y1+[3]x1y2+[1]x0y3

=x3+3x2y+3xy2+y3

(x+y)4=[1]x4y0+[4]x3y1+[6]x2y2+[4]x1y3+[1]x0y4

=x4+4x3y+6x2y2+4xy3+y4

(x+y)5=[1]x5y0+[5]x4y1+[10]x3y2+[10]x2y3+[5]x1y4+[1]x0y5

=x5+5x4y+10x3y2+10x2y3+5xy4+y5

                                        
Pascal's Triangle

We note that the coefficients the numbers in front of each term follow a patter.

Here is the video that I found about Pascal's Triangle:

The Binomial Theorem:

Example: (2x – 5y)⁷

^{I'll plug 2x, -5y, and 7 into the Binomial theorem, counting up from zero to seven to get each term.}

^{Then simplify:}   

I hope this informations help you. Most importantly, our first test is next week on 24th Tuesday, good luck preparing for the test!!! 

-Reedhee Modha