Function f(x) from the graph f'(x)

1. The function is increasing from (-2,0)U(0,2) because between these intervals you get positive outputs. The function is decreasing from (-∞,-2)U(2,∞) because all the outputs in these intervals give you a negative output.


2. I think there are three extrema because at three points the slope is equal to zero. At f'(o) the slope is equal to zero which means it is a critical point. Two other points where the slope is equal to zero is at f'(-2) and at f'(2) which makes them two other critical points.


3. The function is concave up at about (-∞,-1.2)U(0,1.2) because between theses intervals f''(x) is greater than zero. The function is concave down at (-1.75,0)U(∞,1.75) because f''(x) is less than zero.


4. The power function could be -x^5 becuase the f'(x) is negative so i'm guessing would be negative as well. And f'(x) curves four times so the power funtion would be one more up.

Fixed vs. Growth

1. I think i am a little bit of both because I'm always up for learning and expanding my knowledge on everything but then when someone does try to give back "useful" negative feedback, I'll be the stubborn person that i am an just not listen to what they say. But it all depends what they are criticizing about. But the article made me realize how sometimes i will back down from an academic challenge but not a physical one. For example i had pushed myself to get my left lay-ups right and i finally got them down.So it all pays off in the end to push yourself.

2. It's helped me a lot because i was actually thinking of dropping the class but then i challenged myself to stay in the class and pass it. It really helped me push myself and really put the effort that you need to put into the class. And that question card thing helped me too because it made me wanna solve the problems and show everyone what you're made of.

3. I wasn't too surprised because i know how anyone can expand there knowledge. I think people just need to constantly work on it to make it stronger. To me taking those challenging classes its like steroids for the brain :D .

4. It will help me to definitely push myself and follow through all the way to the end instead of giving up half way through the class or in life even.

Algebra vs. Calculus

1. The difference between finding the limit at x= c and plugging in the number x=c is when you find the limit at x=c is when is you're finding the limit as your output values get closer to that constant. When you're plugging in x=c , you re finding the exact answer when you plug in the constant which gives you a specific answer. I dont really know when they're the same so i'm not gonna give a Bee-S answer lol.



2. Finding the slope of the line is similar to finding the derivative because finding the derivative of a curve is equal to the slope of a line. You still use the same concept of rise over run. For example you use y2-y1/x2-x1 to find the slope of line is the same as f(a+h)-f(a)/h to find the slope of a curve. I'm not really sure about the differences except that one is the slope of the line and the other is the tangent line.

Tips and Hints ????????

Transformations
With transformations i first look at what is inside the parenthesis. Whatever is inside the parenthesis will determine what whether you graph shifts to the left or to the right. If there is a negative/subtraction sign it will move to the right and if it is a positive/addition sign then it moves to the left. Then I look at what is outside the parenthesis. If there is a negative/subtraction sign it shifts down. If there is a positive/addition sign then you shift the graph up. It also depends on how many units come after the sign. One thing i try to remember is that for transformations , that Ms. Hwang commonly uses is that they are counter intuitive.

Trigonometry
I think trigonometry is basically centered around the unit circle. If you know all you radians, coordinates, and fractions then you are good. i try to remember that the sections go by 6, 4, 3, 2, then you flip them over on each side of the circle and for Quadrant II is one less than the denominator, Q.III is one more, and Q.IV is multiply by 2 subtract one. And i just remembered, for graphing, that cos(x) that it has a point at (0,1) and sin(x) is at the origin, and they look like speed bumps. For all the other ones i just remember that they have asymptotes .

What Confuses Me
Finding the periods and the domain and range for tan(x), csc(x), sec(x), cot(x), cos(x),and sin(x).

Lincoln Logs and Inverses

What I Understood

• To find the inverse of a function you switch the X and Y and there you go .
• I also learned that you don't have to graph the inverse of a function to see if the inverse is a function or not. You can determine if a function is on-to-one if you try the horizontal line test and if it has more that one point going through one of the lines then it is not one-to-one
• Symmetrical functions have a slope that is consistent .
• The inverse of (f) is (f^-1)
• The base of a log is usually always(oxymoron) 10 unless you have a different base there

What I Don't Understand

• When you have to use log or Ln. Like the equation (1.045)^t=2 and you have to solve for t, i don't get if i would have to use log or Ln for this equation.
• I don't understand how to solve an equation when there is two X's.
• I also don't understand when you have to find the inverse of an equation that is a fraction .
• I don't understand how to graph logs
• I don't get how to solve f(g(x))=x but g(x) is not the inverse of x !!!! Like what does that even mean !!!! that problem confused the hell out of me :T

And it helps that I sit next to Ivan S. because he helps me out a lot when i don't get it. Thanks Ivan =) ....

Even and Odd functions

An even function :
Even functions are functions where the left half of the plane, which would be in quadrant II, looks like the mirror image of the right half of the plane, which is in quadrant I. You can use the equation f(-x)=f(x)or x2. What it pretty much is is that for every X there is a -X in the domain.




An odd function:
And odd function is where the upper right side of the plane, which is quadrant I, is symmetrical to the lower left side of the plane, which is quadrant III. It is symmetrical about the origin.An equation you can use for these type of functions are f(−x)=−f(x) or x3.

Au Contraire !!

Well my name is Jackey. My birthday is on the 4th of October and I'm currently sixteen years old. I dislike rude people =p. I can be pretty talkative, most people who know me already know that about me. Sometimes I annoy myself because i talk to much and i tend to get distracted very easily which is something I'm working on. I'm a huge doodler, especially on myself which people tell me can lead to skin cancer but oh well i cant help myself. I'm a huge adrenaline junkie which tends to get me in alot of trouble. I love reading believe it or not, I'm currently reading East of Eden [great book btw, well so far]. I like playing basketball, with JOYCE especially.
I'm a pretty blunt person. I love all types of music except country. I like old school rap and hip-hop, its not the same now-a-days. My favorite band is The Smiths!!! and Morrissey of course. I hope i didn't get off to a bad start in this class but i kinda feel like a already did especially with the coming late and stuff. Well hopefully i can turn that around.