1. When finding the limit of a function at x = c, you are finding the outputs that gets closer and closer to c from the negative and positive side. This will give you an approximate answer.
When plugging in the number x = c (or f(c)), you are finding the exact output at that number. This is basically your y and now you have a specific point.
One case in which the two are the same is when there is a removable discontuinity. This can be proven by the formula, lim f(x) x -> c- = lim f(x) x -> c+ = f(c). As the points from the negative and positive get closer to x, it will equal to c.
2. Derivatives and a slope of a line are similar because a derivative is the slope of a line. To be able to find the derivative at a certain point, you first need to find the slope of line that points is in. In both, you are finding the change of y over the change of x.
But they are also different because the deravative can be treated as the slope of a tangent line at a certain point, curved or not, but the slope of a line can be any common line.
Saturday, December 19, 2009
Monday, December 7, 2009
My Limit..!
1. Finding a right and left end behavior model for a given function.
I understand it a few times but I need more clarification.
Ex.) f(x)=x+lnx
I know that you need to know how each graph looks like but from there, I get stuck.
2. Questions that involve finding the discontinuity.
I get stuck when it comes to questions like this because I don't know what to do.
Empty dot and fill-in dots throw me off.
Sometimes the questions that use piecewise confuse me.
For example, on Pg. 95, question 29.
I don't know why when x=0 and x=1 it is discontinuous.
3. Finding the horizontal asymptotes.
I sometimes know what they are because I already know how the graph looks like (e.g. f(x)= 1/x).
But I don't know what to do when given a more complex fucntion.
I rememeber one question I had trouble with was the last Free Response on our last test.
I forgot the function but I remember I couldn't find the horinzontal asymptotes.
I understand it a few times but I need more clarification.
Ex.) f(x)=x+lnx
I know that you need to know how each graph looks like but from there, I get stuck.
2. Questions that involve finding the discontinuity.
I get stuck when it comes to questions like this because I don't know what to do.
Empty dot and fill-in dots throw me off.
Sometimes the questions that use piecewise confuse me.
For example, on Pg. 95, question 29.
I don't know why when x=0 and x=1 it is discontinuous.
3. Finding the horizontal asymptotes.
I sometimes know what they are because I already know how the graph looks like (e.g. f(x)= 1/x).
But I don't know what to do when given a more complex fucntion.
I rememeber one question I had trouble with was the last Free Response on our last test.
I forgot the function but I remember I couldn't find the horinzontal asymptotes.
Wednesday, November 25, 2009
Majors and Colleges
Majors
1. Accounting and Business Management: This major includes studies in the both business and accounting administration. You will have to know math because you will work with money and need to know how much money you made or how much you lost. Also, you will need to know how to manage a business. You have to make decisions in which will be good for the company, like hiring more people or firing an employee for not making any productivity.
2. Sports and Fitness Administration: This major includes learning how to use business and legal principles to run athletic programs, health clubs, and sports teams. You will need to know how to promote a sporting event or fitness centers to attract as many as people as you can. You will also need to deal with contracts and learn how to create a budget. Learning the body and the ways in which it can healthier is also another thing that is included in this major.
3. Film Production: This major includes dealing with other people to come up with a movie that everyone would want to watch. You will also study other movies to get ideas that will make your movie the best. You really have to motivated because you are going to use your own money to pay for the equipment, spend a lot of time editing scenes, and be able to take criticism from others.
Colleges
1. ITT Technical Institute: Sylmar
To attend, all I need is a High school diploma , or a GED. It is an urban setting with a population over 500, 000. There are about 1,000 undergrads that are all seeking a degree. There is no application fee. To be to transfer to this college, you need at least a 2.0 GPA.
2. Pepperdine University
Located in Malibu, CA. It is in a suburban setting in a small city. There about 3,404 undergrads and 3,386 are seeking a degree with 782 of those being freshmen. Mostly men (54%), white/non-hispanic (64%). Most of the students there had a GPA of 3.75 or higher in high school.
3. California State University: Long Beach
The regular application fee is $55. About 42% of the people that aplly are acceptated and only 86% of students return for their sophomore year. You need at least a GPA of 2.0. Mostly Hispanic (34%) and all students were in the top half of their graduating class.
1. Accounting and Business Management: This major includes studies in the both business and accounting administration. You will have to know math because you will work with money and need to know how much money you made or how much you lost. Also, you will need to know how to manage a business. You have to make decisions in which will be good for the company, like hiring more people or firing an employee for not making any productivity.
2. Sports and Fitness Administration: This major includes learning how to use business and legal principles to run athletic programs, health clubs, and sports teams. You will need to know how to promote a sporting event or fitness centers to attract as many as people as you can. You will also need to deal with contracts and learn how to create a budget. Learning the body and the ways in which it can healthier is also another thing that is included in this major.
3. Film Production: This major includes dealing with other people to come up with a movie that everyone would want to watch. You will also study other movies to get ideas that will make your movie the best. You really have to motivated because you are going to use your own money to pay for the equipment, spend a lot of time editing scenes, and be able to take criticism from others.
Colleges
1. ITT Technical Institute: Sylmar
To attend, all I need is a High school diploma , or a GED. It is an urban setting with a population over 500, 000. There are about 1,000 undergrads that are all seeking a degree. There is no application fee. To be to transfer to this college, you need at least a 2.0 GPA.
2. Pepperdine University
Located in Malibu, CA. It is in a suburban setting in a small city. There about 3,404 undergrads and 3,386 are seeking a degree with 782 of those being freshmen. Mostly men (54%), white/non-hispanic (64%). Most of the students there had a GPA of 3.75 or higher in high school.
3. California State University: Long Beach
The regular application fee is $55. About 42% of the people that aplly are acceptated and only 86% of students return for their sophomore year. You need at least a GPA of 2.0. Mostly Hispanic (34%) and all students were in the top half of their graduating class.
Saturday, November 21, 2009
Tips and Hints..
1. Transformations
When I look at something like f(x+3)-2, I first consider what is inside the parenthesis. Whatever is in the parenthesis will determine how the graph will shift horizontally. Since there is a +3, the graph will shift to the left by 3. You will think that because it a positive number you would shift the graph to the right but NO. I just remember to do the opposite when I am looking inside the parenthesis.
Next, I look outside the parenthesis to determine how the graph will shift vertically. Now that I am not looking inside the parenthesis, I can go with my normal instincts and shift the graph up or down by the number indicated. In this case, there is a -2, which means the graph will move down by 2.
If I am looking at another function like sin(2x), I again look what is inside the parenthesis. In this case, a number is now being multiplied by x, rather than being added/subtracted. If the number is a whole number, then the graph will be compressed horizontally. If it's a fraction, then the graph will be stretched-out. Once again, think the opposite.
2. Trigonometry
When it comes to the unit circle, I don't have a hard time remembering where everything goes. If I am trying to find the coordinates of each pi, then I just remember that the short sides are 1/2 and the long sides are 3/2. That leaves the sides that are 2/2. From there, I just insert a negative if it is necessary. If I know that, then I can find where the pi's go. For all the coordinates that have 3/2 as the x, it is _pi/3. The coordinates that have 1/2 as the x, it is _pi/6. The rest are _pi/4. It all comes to me when I see the unit circle on paper.
With graphs, I remember that cosx will always have the point (0,1) and sinx will have (0,0). I know the curves for both, so I don't have a trick to remember that. For the rest, tanx, cscx, secx, cotx, I keep in mind that all are going to have asymptotes.
3. What confuses/worries me
The inverse graphs still troubles me because I don't remember the domain and range for most of them. I sometimes forget that I am supposed to switch x and y values. That means that the range will include pi's and the domain will not.
When I look at something like f(x+3)-2, I first consider what is inside the parenthesis. Whatever is in the parenthesis will determine how the graph will shift horizontally. Since there is a +3, the graph will shift to the left by 3. You will think that because it a positive number you would shift the graph to the right but NO. I just remember to do the opposite when I am looking inside the parenthesis.
Next, I look outside the parenthesis to determine how the graph will shift vertically. Now that I am not looking inside the parenthesis, I can go with my normal instincts and shift the graph up or down by the number indicated. In this case, there is a -2, which means the graph will move down by 2.
If I am looking at another function like sin(2x), I again look what is inside the parenthesis. In this case, a number is now being multiplied by x, rather than being added/subtracted. If the number is a whole number, then the graph will be compressed horizontally. If it's a fraction, then the graph will be stretched-out. Once again, think the opposite.
2. Trigonometry
When it comes to the unit circle, I don't have a hard time remembering where everything goes. If I am trying to find the coordinates of each pi, then I just remember that the short sides are 1/2 and the long sides are 3/2. That leaves the sides that are 2/2. From there, I just insert a negative if it is necessary. If I know that, then I can find where the pi's go. For all the coordinates that have 3/2 as the x, it is _pi/3. The coordinates that have 1/2 as the x, it is _pi/6. The rest are _pi/4. It all comes to me when I see the unit circle on paper.
With graphs, I remember that cosx will always have the point (0,1) and sinx will have (0,0). I know the curves for both, so I don't have a trick to remember that. For the rest, tanx, cscx, secx, cotx, I keep in mind that all are going to have asymptotes.
3. What confuses/worries me
The inverse graphs still troubles me because I don't remember the domain and range for most of them. I sometimes forget that I am supposed to switch x and y values. That means that the range will include pi's and the domain will not.
Saturday, November 14, 2009
Inverses and Logs
Recap 4 major concepts that you have understood about either/both of these two topic
1. I understand how to find the inverse of function. If you are trying to find the inverse of f(x)= 2x+3, then all you will need to do is convert it to an equation, y= 2x+3. Next, get x by itself. This will give you x= y-3/2. Now switch x to f^-1(x) and y to x. This will give you f^-1(x)= x-3/2, the inverse of f(x)= 2x+3.
To verify this, you will need to plug in f^-1(x)= x-3/2 into f(f^1(x)) and f(x)= 2x+3 into f^-1(f(x)). Both should reduce to be x. If not, then it is not the inverse of the function.
2. I understand the concept of "one-to-one." The horizontal line test is used to determine if the graph of a function and its inverse are actually "functions". You do not need the graph of the inverse to be able to do this test, you only need the original graph. If the graph only touches the horizontal line test at one point, then the function is "one-to-one."
3. I understand logarithmic expressions, somewhat. For example, in the expression log416, the base is 4. To solve this problem, you would re-write it as 4^x= 16. Then solve for x. The equation will change to 4^x= 4^2. You can now eliminate the 4 from each side and all you are left with is x= 2.
4. I understand that if you are not given the base in a logarithmic expression, the base is automatically 10. For example, the expression log100 would be re-written as log10100.
Write about what you did NOT understand completely
1. I do not know how to graph logarithms. I couldn't solve the problems #39-42 on page 44. I get confused what to do when there is an "ln."
2. I also get stuck on problems that involve e or ln. For example, in the problem ln(y-1)-ln2=x+lnx, I do not know the final answer should look like or how to simplify completely. I try to solve this problem by first subtracting ln2 from both sides and turning ln(y-1) into loge(y-1). Next, I used one of the log rules to turn ln2+lnx+x into loge(2+x)+x. Then I cancelled loge from both side and got y-1=2+2x. From there I got y=2+3 but I do not know if that is the right answer.
1. I understand how to find the inverse of function. If you are trying to find the inverse of f(x)= 2x+3, then all you will need to do is convert it to an equation, y= 2x+3. Next, get x by itself. This will give you x= y-3/2. Now switch x to f^-1(x) and y to x. This will give you f^-1(x)= x-3/2, the inverse of f(x)= 2x+3.
To verify this, you will need to plug in f^-1(x)= x-3/2 into f(f^1(x)) and f(x)= 2x+3 into f^-1(f(x)). Both should reduce to be x. If not, then it is not the inverse of the function.
2. I understand the concept of "one-to-one." The horizontal line test is used to determine if the graph of a function and its inverse are actually "functions". You do not need the graph of the inverse to be able to do this test, you only need the original graph. If the graph only touches the horizontal line test at one point, then the function is "one-to-one."
3. I understand logarithmic expressions, somewhat. For example, in the expression log416, the base is 4. To solve this problem, you would re-write it as 4^x= 16. Then solve for x. The equation will change to 4^x= 4^2. You can now eliminate the 4 from each side and all you are left with is x= 2.
4. I understand that if you are not given the base in a logarithmic expression, the base is automatically 10. For example, the expression log100 would be re-written as log10100.
Write about what you did NOT understand completely
1. I do not know how to graph logarithms. I couldn't solve the problems #39-42 on page 44. I get confused what to do when there is an "ln."
2. I also get stuck on problems that involve e or ln. For example, in the problem ln(y-1)-ln2=x+lnx, I do not know the final answer should look like or how to simplify completely. I try to solve this problem by first subtracting ln2 from both sides and turning ln(y-1) into loge(y-1). Next, I used one of the log rules to turn ln2+lnx+x into loge(2+x)+x. Then I cancelled loge from both side and got y-1=2+2x. From there I got y=2+3 but I do not know if that is the right answer.
Saturday, November 7, 2009
Even and Odd Funtions
Even Functions
The equation, f(-x)=f(x), is used to define an even function.
For every input, (x) or (-x), the output (y) will always be the same.
- The x can be either negative or positive but the y will come out the same.
This results in the graph being symmetrical about the y-axis.
- A graph in Quadrant 1 would be reflected onto Quadrant 2, as if it was flipped by a mirror. (Also, can work for Quadrant 3 and 4.)
Example:
The graph above is x^2.
If 2 was plugged in, (x) , then the result will be 4, (y).
If -2 was plugged in, (-x), then the result will still be 4, (y).
Odd Functions
The equation, f(-x)=-f(x) , can be used to define an odd function.
The graph will be symmetrical about the origin.
- A graph in Quadrant 1 would be reflected onto Quadrant 3, as if it was flipped diagonally. (Also, can work for Quadrant 2 and 4.)
Example:
The graph above is x^3.
If 2 was plugged in, (x), then the result will be 8, (y).
If -2 was plugged in, (-x), then the result would be -8, (-y).
If (x,y) exists on the graph, then point ( -x, -y) also has to exist.
- This goes for the same for (-x,y) and (x, -y).
Saturday, October 31, 2009
Well.. my name is Javier Hernadez. No middle name. I have only one brother and his name is Jacob. He can be annoying at time but whose sibling isn't? My dad is from Mexico and my mom is from El Salvador. Both of my parents have improved my life in some sort of way. My dad has pushed me to do my best since I was young and can still remember that belt of his everytime I did something bad. My mom is supportive and even though we don't get along all the time, she is still there for me when I have any kind of problems. Without my parents help, I would be that kid that gets bad grades and does nothing with their life, so I thank you mom and dad.
I like to watch/play every kind of sports, but the sport that catches my attention is basketball. I first picked up a basketball when I was in 4th grade but got interested in it when I was in 8th grade. I play basketball because it is an interesting sport. Basketball is always interesting because there is constant scoring (not like soccer, no offense) and a team can be leading by 15 points but in a quick minute or two, they can be down by 5 points! That is why a player must always be playing hard and not take a single brake until the clock says 0. My favorite basketball team are the Los Angeles Lakers. I bleed purple and gold. I was so happy when the Lakers won their 15th championship this past June. I hate when people say that the Lakers suck because they don't. I will defend the Lakers in any way possible.
I like math since I can remember. I may have trouble at it sometimes but I eventually find a way to get a good grade. I like math because I feel good inside when I am giving a problem and I find a solution. The subject that I dislike the most is English. I think the reason why I don't like English is because I have to write essays and that bores me. I may not like English but I'm still taking AP American Literature. I have also taken a First Responder class and I'm currently a Level 2 CFR. I have signed up to work at the Rose Parade in January.
I like to watch/play every kind of sports, but the sport that catches my attention is basketball. I first picked up a basketball when I was in 4th grade but got interested in it when I was in 8th grade. I play basketball because it is an interesting sport. Basketball is always interesting because there is constant scoring (not like soccer, no offense) and a team can be leading by 15 points but in a quick minute or two, they can be down by 5 points! That is why a player must always be playing hard and not take a single brake until the clock says 0. My favorite basketball team are the Los Angeles Lakers. I bleed purple and gold. I was so happy when the Lakers won their 15th championship this past June. I hate when people say that the Lakers suck because they don't. I will defend the Lakers in any way possible.
I like math since I can remember. I may have trouble at it sometimes but I eventually find a way to get a good grade. I like math because I feel good inside when I am giving a problem and I find a solution. The subject that I dislike the most is English. I think the reason why I don't like English is because I have to write essays and that bores me. I may not like English but I'm still taking AP American Literature. I have also taken a First Responder class and I'm currently a Level 2 CFR. I have signed up to work at the Rose Parade in January.
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