Tips and Hints

TIPS AND HINTS

1. There's really nothing special about how I remember transformations. However, there is a step by step process that I follow when I need to graph them. The first thing I do is find the original graph (by removing the transformations) and in my head, I picture how the graph looks. After that I start to add in the transformations as I go.

- when a number greater than 1 is in front of the x [ex. cos 3x] then the input will be multiplied and the whole graph will shrink on the x-axis.

-when a fraction is in front of the x [ex. cos 1/2 x] then the input will be reduced and the whole graph will expand on the x-axis.
[[This affects the period of the graph]]

-when any number is subtracted from the input and is in parenthesis, then it will shift the graph to the right.

-when any number is added to the input and is in parenthesis, then it will shift to the left.

-when any number is subtracted from the input and is NOT in parenthesis, then it will shift down. -when any number is added to the input and is NOT in parenthesis, then it will shift up.


2. How I remember trigonometry is much easier. If I need to find an angle, lets say sin 1/2, all I have to do is remember on what quadrant sin is positive. Then I think back to the unit circle and remember when sin (Y) is equal to 1/2. After all that, I find out the angle is equal to pie/6 and 5pie/6.
A neat trick that I know for remembering the positive values in the unit circle is "ALL STUDENTS TAKE CALCULUS"

In quadrant I: ALL of the values are positive.

In quadrant II: Sine is positive

In quadrant III: Tangent is positive (-sin x/-cos x)

In quadrant IV: Cosine is positive.




3. What doesn't really confuse me but does worry me about trigonometry are the sec -(x), csc-(x), and cot-(x) graphs. They are still not well engraved in my head.

Online Graphing Calculator...

Have you ever thought about what will happen when they take away our magic graphing calculators at the end of the year? Well, I have! So I found this cool online calculator. Its really simple and easy to use.
Check it out. Here's the link: http://www.mathsisfun.com/data/graph.html
But remember, don't become too dependent on graphing with calculators!

To a fellow classmate :D

Each bullet point is a step for solving this problem :)

-Given

-5 root of 36 is the same as 36^1/5 (Simplifying).

-Simplifying some more. (ex. 1/x is the same as x^-1).

-Since the base is 6, you want to simplify 36 to 6^2.

-Rule of Exponents: Multiply the exponent 2 with the outer exponent -1/5


*Drum Roll* And the answer is -2/5!

I tried to make this easy to understand. I strayed away from other mathematical terms when explaining. Hope I helped!

Inverses and Logarithms :(

1. Four major concepts that I learned/understand about Inverses and Logarithms.

• Regarding Inverses, I understood the concept of "one-to-one" fairly well. The partner work really helped me understand that to find the inverse of a function one must simply switch the output with the input and it must pass the "horizontal line test" to be considered one-to-one. [That being said, I understood all of homework C1.]
• Also regarding Inverses, I understood that when you find an equation for the inverse function it is very helpful to verify your answers. "f( f-(x)) = f-(f(x)) = x" [Verifying makes me feel better than looking at the back of the book to check if my answers are correct.]
  
• Moving on to Logarithms, I understood the "story" Ms.Hwang showed us on the board. I thought it was very cool and it helped me understand how to get rid of the logarithm and solve for a variable. [However, I still think I need a bit more practice on solving for variables when there are logarithms in the equation]
  
• I also understood the rules of logarithms such as the product rule, quotient rule and power rule.
  

2. What I did not understand...

First of all I have to say that some of the questions on homework C2 gave me a really hard time.

• One thing I do not really understand are solving equations with "e". For example (Homework C2 pg.44 #35 & 36). This question asks to solve the equation algebraically and to support the solution graphically. The equation is e^x + e^-x = 3. This is how I tried to solve the problem:

e^x + e^-x = 3
lne x + lne -x = ln 3
x + -x = ln 3
loge x + loge -x = loge 3 (loge)

I didn't know how to multiply ^^^^ that so I gave up.

On #36 I solved the equation further but only got up to: log2 (-x) = log2 5/2

• Another thing that I completely did not understand was how to graph a logarithm equation. Because I did not know how, I was not able to answer straight-forward questions such as "finding the domain & range"-- This was very frustrating for me.

This practically covers most of what I did and didn't understand regarding Logarithms and Inverses. P.S: If you know how to solve any of these, please help me!

EVEN and ODD Functions!

EVEN Function(s)

GRAPHICALLY, an even function is a function that is symmetrical about the y-axis. Meaning that Quadrant 1 & 2 or 3&4 are like a mirror view of each other. Some examples of even functions are the cos x graph or even a parabola:

What makes these graphs symmetrical about the y-axis or in other words even, is due to the algebraic form of the even functions.

ALGEBRAICALLY, an even function of x is defined as f(-x) = f(x)
- The input, whether it be negative (-x) or positive (x), will share the same output. Having said that, it would be similar to the points (-1,1) and (1,1) or (1,-1) and (-1, -1).
- The x (input) could change but the y (output) will remain the same, making the two points reflect themselves on the y-axis.

ODD Function(s)

GRAPHICALLY, an odd function is a function that is symmetrical about the origin. The graphs of sin x and f(x) = x are good examples of odd functions. Quadrant 1 & 3 or 2&4 are reflected diagonally in any odd function.




ALGEBRAICALLY, an odd function is defined as f(-x) = -f(x)
- For example, if a point (1,1) lies on a graph, then the opposite points (-1,-1) must also lie on that graph. If (-1, 1) lies on a graph then you will also find (1,-1).


I tried to explain even and odd functions using points with one unit, because that was how I was better able to understand these functions. Comment me if you have any questions.

About Me

Hello everyone! My name is Rocio and I am going to tell you a little bit (ok a lot) about myself. I am sixteen years old as of Oct 26. I have two siblings: a nine year old brother named Tony and a seventeen year old sister named Julie. I enjoy playing soccer as much as I enjoy coming to school. Here at Poly I am involved in tons of activities. I am the vice-president of the National Honors Society for 11th grade C-track, historian for the Soccer Club, I have been in CSF for three years, and I am on the soccer and track team as well as being involved in many other clubs. I have volunteered for city council campaigns and I am a member of the Young Senators Program. I must also tell you that I LOVE going on road trips. I find enjoyment in looking at the different environments in which people live. About 2 months ago I went on an amazing road trip to my hometown in Mexico (I like to pretend I was born there) and I took a lot of pictures.



LOOK AT THIS COOL SNAIL!! IT WAS HUGE!






This was my destination; my father's hometown. It's a little town called "Mesillas" and the closest city is about 20 miles away. Due to its detachment from the city, Mesillas has NO internet, NO phone service (only a couple of telephones in town-I have no idea how they get service) and VERY little technology. And this is why I LOVE it.
Believe me, there are tons of things to do without technology!!!



I hope that by reading this you will all learn a little bit more about me. Don't be shy and feel free to talk to me :)