Colleges

1. There are quite a few things that I would like to major in now that i look at the list of majors. Wow it is very hard to pick only three.

• One major i would like is Aerospace Engineering. This major is mostly about using math science to design and develop air craft and space craft. They also study aerodynamics, launch, flight controls, and learn about engines.
• Astrophysics is also something that I am interested in. This is basically the study of galaxies and stars. In astrophysics, people study about the life cycles of stars and the matter between stars.
• Computer Engineering is another major that I am interested in. This major is about learning how lo analyze, design, and develop computer hardware and software.

2. These are some of the colleges that interest me, mainly because they involve some sort of engineering major, and they are also in California.

• UCLA...

1. it is a 4 year public university
2. Urban setting
3. 90% of students are in-state
4. applicants admitted 23%
   

• UC Berkeley

1. public 4 year university
2. urban city
3. small city
4. applicants admitted 22%

• San Francisco State University

1. Public 4 year university
2. urban setting
3. applicants admitted 66%
4. 98% in-state students
5. calendar goes by semesters
   

Tips and Hints

1. How I remember transformations.

• I know that transformations have to do with how graphs shift. I remember that if you add a number to the output of the function the graph shifts up and if you subtract it the graph moves down. For example f(x)=x+3 in this example the graph moves up 3 spaces up. If you add something to the input, the graph could either move to the left or the right. For example f(x)=(x+5), in this graph the graph shifts 5 units to the left. What I use to remember where the graph shifts is whether the number you are adding is inside or outside of the parenthesis. If it is at the outside of the parenthesis the graph could move either up or down. If it is in the inside, the graph shifts to the left or right. If the exponent is a negative the graph is automatically flipped vertically. For example y=-x+4. This graph is flipped vertically.

2. How I remember trigonometry.

• Trig. is basically all about the unit circle. you basically have to memorize the unit circle. You have to know from 0 to 2pie. There are 16 important radians. each one of these radians has a certain coordinates. When asked anything about the unit circle, for example sin of pie/2. One of the most important things to know is that sin stands for the y coordinate and that cos is for the x coordinate. if you know the coordinates of each radian, problems like this should be easy. In order to graph them, again you need to know the coordinates of each radian. if you are asked to graph f(x)=sin(x), you have to plug in the radians starting with 0 aka 2pie. sin of 2pie is 0. then go to pie/6, sin of pie/6 is 1/2. if you continue this process you can graph this function easily.

3. What worries me.

• what worries me the most... I would have to say that graphing logs. I understand how to graph them and all but unfortunately it takes me too long to graph them. It takes me way too long to figure out how the graph looks. It is very time consuming, when it gets too complicated, I don't have that much patience and I may give up. That is the only problem i have so far.
  

Inverses and Logarithms

What I know

One thing that I understand is that the common base for logarithms is base 10.

• when there is an equation that does not show a base after the log, it means that the base is 10 for example log(x)

I also understand that the common base for natural logs (ln) is e

• when you see something like ln(5) there is an invisible e as base
  

Another thing that i understand is how to solve basic equations with logarithms in them.

• if you wanted to solve an equation like log(100)=x, all you have to do is carry the invisible log base under the x making it 10^x. after you do that you are left with 100=10^x. all that is left to do is to make both bases similar. for example 10^2=10^x making 2=x

Finally I now fully understand the difference between exponential functions and power functions

• in order to solve an exponential function, for example 2^x, you would need tot use a logarithm to solve it.
• for a power function like x^2, you need to do the square root of x

What I dont understand

I am having a difficulty in graphing logarithms. I am also having great trouble finding more complex inverses like f(x)=2X+1/x+3

Even and odd functions

An even function is basically a function that when graphed it looks symmetrical about the y axis.

• a great example of this would be a parabola.

• since parabolas look similar on both the negative side and the positive side, they are considered even functions.

• An odd function is a function that when graphed, the graph is symmetrical on the quadrant diagonal.
• all it is, is an even function except that one side of the graph is flipped either down to the lower quadrant or up to the upper quadrant.
  
• This can be seen by simply graphing any function with odd exponents.
• What the odd exponent does is that it flips one side of the graph down making it an odd function.