F(x) from F'(x)

1. f(x) is increasing between [-2, about 1.3)U[0, about 1.3). I could tell this is the answer from the graph shown because wenever f'(x) has a positive output is where f(x) is positive.

2. local min at x= -2
local max at x= 2
Extrema can only occur when f'(x) is equal to 0 or is undefined, which is characterized by those two points. At x= -2 the sign changes from negative to positive therfore it being a local min. At x=2 the sign changes from positive to negative therefore being a local max.

3. The function f(x) is concave up at (-1,1) and convave down from (- infinity, -1)U(1, infinity). A function is concave up whenever f"(x)>0 and concave down when f"(x)<0. you can tell Weather its concave down when you see the graph of f'(x) is decreasing and concave up when the graph of f'(x) is increasing.

4.The graph of f'(x) would defenitly be a polynomial equation to the 4th power, now taking in consideration that the graph is the derivative of the origional graph f(x) must be a polynomial to the 5th power. p.s I looked at the notes ms.hwang gave us on how to tell how a polynomial equation would look if its higher than an equation to the 3rd power.

Fixed vs. Growth Mindset

1. When it comes to "intelligence" i think i have a growth mindset. I see "intelligence" as something everyone can be at a high level if everyone has dedication to what they do not caring of what everyone thinks of you. The reading tells me that i am because I personlay like challenges, i think they help you understand a certain subject more. I really don't mind of others critisism, unless its of my work i will pay attention an learn from my mistakes.
2. This mindset has helped me in math because it has allowed me to attend the class I am attending right now, calculus. If it was'nt for this mindset i would have stoped at what was requiered to graduate High School, but i decided to out do myself. This mindset has hurt me because sometimes for trying to outdue myself i tend to get low grades in class and grades in tests that i have never gotten in math. :/
3. Well i personally already knew that the brain is just like any muscle that can eventually be trained. There is no stupid person, its their efforts that ar stupid not the person.
4. This will affect my future because now i know that any challlenge in life i take to see what exactly i am capable of.

algerbra vs. calculus

1. Well the difference between finding the limmit of a function at x=c and plugging in the number x=c is really nothing if you are finding the limit of a continuous function becasuse you will either way get the same answer, but when the function is discontinous it REALLY MATTERS.
When its a discontinous function you dont plug in the number x=c because when the function is discontinuous at a certain point, or otherwise has a jump, an empty hole(removeable discontinuity), or infinite discontinuity, you wont just be able to plug in (c) because you will get an exact output, and if the function is discontinuous there will be no exact output, thats why you find the limit of x=c becasue that will give you a y value as x=c.

2. Finding the slope and the derivative is basically the same thing because they both give you the rat at which the graph is moving. They are different because slopes are mostly used for lines and derivatives are used for for complicated functions, one example is x^3. A tangent line and a secant line is required to find the derevative of a function, thats why you can not find the derivative of a line. A tangent line is a line at the function at one point, and a secant line is a line on the graph at 2 points.

CAUTION:

THE EXPLANATION AT THE TOP MAY BE A LITTLE CONFUSING, THE WRITER IS NOT RESPONSIBLE FOR ANY HEAD ACES, OR NAUTIOUS SYMPTOMS.

lol j/k :D

LIMITS!!

1.Horizontal asymptotes
horizontal asymptotes is something i dont really get, i mean sometimes i know because i know how the graph looks like but what do i do when i dont know how it looks like? I mean if i use my calculator i could find it but im not allowed to in tests. In the last freeee response in the test i had trouble in the part where it said to state the horizontal asymptote. :-/
2. Behavior of f(x) to the left and to the right of the asymptote
When it comes to end behavior models i completely understand how to find them, but when it asks to describe to describing the behavior graphically of f(x) to the left and the right is when i get stuck :0
3.CONTINUITY AND DISCONTINUITY
ok, discontinuity and discontinuity i sometimes feel safe about, but most of the time i forget what to do or i just go blank. If anyone has an easy way to remember what this is PLEASE tell me D:

Clleges!! :O

1. the first major i found that interested me is Restaurant and food services managment, in the buisness major. I learned that tis major can make someone manage a small coorporation or basically any food service.

the scond one that i found that interests me is the is the culinary arts major. I learned that entering this major can sometimes make or brake peoples decision in finishing this major because of all the critisism and long hours you have to put into this.

the last major that i found that interests me is the Entrepreneurial Studies major. I found out that being an entrepreneur can make peoples lives easier because they usually always think of something that will improve or make people's lives easier.

2. One university that caught my attention was University of San Francisco. This specific university caught my attention because it is in california but yet it is not in LA. I learned that there is only 15% of hispanics and 39% of the students there are male. I also found it kind of interesting that onlly 29% of the students graduated HS with a 3.7 or higher.

Another college that interested me was the Art Institute of California: Los Angeles. I have heard of this place a lot through comercials and through visitors that have gone to poly and this school for some rason really really interests me! hahha The only thing that is holding me back is that i learned that if i major in this i can't major in something else that intrests me like another major in business but i really like this school

The third school that interested me was the Art Institute of California: Orange County. I think i like this one better than the one at the top although they are the same but in different countys. I like this one better because in this one you can stay in the university n get a bacholers degree, i think i misspelled it :O. I learned that 4 of the students are hispanic, 52% are men, and 25% are part time students. I LIKE THIS ONE ALREADY hahah :D

TIPS & HINTS

1. I found transformations easy to remember, how i remembered them is that when a number is being addd or subtracter to X inside parenthesis the graph shifts to the left or right. Now the tricky part is this, if the number is being added it moves to the left,the negative side, and if it is being subtracted it moves to the right, the positive side. The other thing is that if a number is being addd or subtracted out of the parnthesis, it is gona shift up or down. This one is not like the other, if it is added it moves positive, up, if it is subtracted it moves negative, down.
2. Now about trigonometry, i memorizd it because well mr. kind drilled it in our heads hahah.....thats the only reason i memorized it because he taught it to us for a long time untill everyone got it. All i can honestly say is that if you dont get it, ask Ms. Hwang or any of your past teachers to help you.
3. Hmm what troubles me right now is solving for natural logs. I still cant quite memorize how to solve for them completely.

Logs and inverses

1. Well lets start with inverses. From this subject i understood the concept of one-to-one fast and with no problems. I understood that in order for a a one-to-one to come about, f(x) needs to be a function and so does its inverse, f^-1(x). To test if f(x) is a function the vertical line test has to be done, if for every line only one point is touched by it then it is considered a function. Now that we know f(x) is a unction we need to confirm it being a one-to-one so we have to use the horizontal line test on f(x) to see if its inverse, F^-1(x), is also a function. For the horizontal line test, if no more than one point is touched in a line then it is also considered a function, therefore it is a ONE-TO-ONE.

2. Continuing with inverses, i also understood that the inverse of its parents function is always parallel to the parent function. Lets take for a fact x^2, this is a parabola rite? and it kind of looks like this...

Now the inverse of this function looks like this...

do you see the connection between these two graphs? Both are parallel and we can see that if we graph y=x, the inverse of the parent function is just a reflection of the parent function.

3. Staying on the topic of inverses, i understood how to find the inverse of a function. To find the inverse of a function, f(x), u need to replace x with y and solve for y. Lets take the problem f(x)=3x-2. First you set the equation to x=3y-2 and then you ad 2 to the other side to cancel out the 2 on the right side leaving you with 2+x=3y. Now you divide by 3 to give you 2+x/3=y. Simple as that, now you have the inverse which is 2+x/3=y.

4. In logarithms i learned that the inverse of any exponential function is always going to be a logarithm, for example the inverse of f(x)=5^x is going to be log 5 x.

• What i really do not get at all is how to graph logarithms. For me it is just a little too complicated.
• I really get this but not the problem that is found in HW C2 number 44, f(x)=50/1+1,1^x