Hey there classmates ! this is carjelu and i will talk about symmetry, reflections and inverses.

So we learned today that if you replace x with -x in the equation y = f(x) the graph will be reflected in the y-axis.

For example:

f(x) = x³

f(-x) = (-x³)

Take note that the reflection in y-axis makes x-value negative !

When y is replaced with -y in the equation of a function y = f(x) , its graph will be reflected in the x-axis.

For example:

f(x) = x²

-f(x) = (x²) -> f(x)= -(x²)

Take note that reflection in the x-axis make y-values negative !

When x is interchanged with y in the equation of a function y= f(x), its reflected in the mirror line y = x. This is called an inverse function.

we also learned the steps on how to find the inverse equation:

1. Replaced f(x) with y.
2. Switch x and y.
3. Solve for y.
4. Replace y with f-1(x).

We were given the function of f(x) = 2x + 2 and we have to graph it and its inverse. Then we determine the algebraically equation of the f-1(x).

the black line is called the mirror line where x = y

(1,4) => (4,1)

(0,2) => (2,0)

(-1,0) => (0,-1)

f(x) = 2x + 2

y = 2x + 2

x = 2y + 2

x - 2 / 2 = 2y / 2

y = x - 2 / 2

f-1(x) = 1x/2 - 1

Take note that reflection in the mirror line switch x and y values !

Transformations Effect on Graph

-f(x) reflection in x-axis

f(-x) reflection in y-axis

f-1(x) reflection in y=x

Symmetry

a graph is said to be symmetrical through an axis or the origin if either side is the mirror image of the other .

A function f(x) is even if for any value "x" f(-x) or -f(-x) = -f(x). Even functions are symmetric about the y-axis. This mean that positive and negative x-values result in the same y-value.Even functions would be symmetrical between quadrants I and II or quadrants III and IV.(example is vertical parabola)

A function f(x) is odd if a any value "x" f(-x) = -f(x) or f(x)=-f(-x). Odd functions are symmetric about the origin. This means that positive and negative x-values result in different y-values. Odd functions would be symmetrical between quadrants I and II or quadrants III and IV.(example is a vertical cube)

that would be it :D bye . . . .

Hall of Famer for September

Please cast your votes for the hall of famer of the month.

September 29, 2011

Hi, this is roxanne and our latest lesson was about stretches and compressions.

y=af(x) stretches vertically a is greater than 1.
y=1/af(x) compresses vertically 1 is greater than a.

For example, f(x)= x3 and 2f(x),

The red one is being times by 2 and x stays the same.








You could graph this by:



y=f(bx) compresses horizontally b is greater than 1

y=f(1/bx) stretches horizontally 1 is greater than b

( "read b values as opposite")

For example, f(x)=x2 and f(1/2x),

The red one is being times by two since the opposite of 1/2 is two. And this time y stays the same.

You could graph this by:

I hope everyone had a good weekend! :) Bye.

Hi this is Karla, Last wednesday, we start a new unit which is Unit 2 Transformations. The first topic that we learned from this is Translations.

It has two shifting rules:

• Vertical Translations

y=f(x)+k graph up k units

y=f(x)-k graph down k units

• Horizontal Translations

y=f(x-h) graph right h units

y=f(x+h) graph left h units

example: y = x^{2 and} y = x² + 1

Note:

* Always read h values as opposite *

example:

h value will graph moving 2 points to the right . and k value will graph 3 points moving up.

General Solutions of Trigonometric Equations 2 (sept.22/2011)

Hi this is orit , and im here to go over our latest lesson!

There are many parts to this lesson and they must be done carefully

For example..
sin3Ө=-√2/2

Our first step would be to rationalize √2/2, and we will get -1/2.
Sin = O/H
When we have -,+ 1 as a opposite and 2 as a hypotenues, 45 degrees will be the angle which is π/4.
Sin is negative in Q3 and Q4, that is where the right angle triangles will be placed.



We know that our angle is 45 degrees and its in QIII and QIV, so our next step would be to add π to π/4 and subtract 2π from 5π/4 which equals to 7π/4

Next , we will be adding our [5π/4 + 2kπ, 7π/4+2kπ]

In order for us to get rid of the 3 , we must multiply the denominators by 3.
3Ө= 5π/4x3 + 2kπ/3, 7π/4x3 +2kπ/3

The final answer is

[Ө= 5π/12 + 2kπ/3, 7π/12 +2kπ/3 , where K€I]

Solving Trigonometric Equations on a Specified Interval 2

Helloo, this is mandeep! Today's class we learned about how to solving trigonometric equations on a specific interval 2. We solved some examples and find out how to solving theta(Θ) over the interval.
For example:- 2sin ² Θ = 3sinΘ - 1 over the interval 0 ≤ Θ ≤ 2π

To solve this equation ,we have to know how to do factors.(find two factors that when we multiply to 2 is + and if we add will be -).
2sin ² Θ = 3sinΘ - 1
2sin ² Θ - 3sinΘ + 1=0
(2sinΘ-1)(sinΘ - 1)=0

(2sin Θ-1)=0 and (sinΘ-1)=0

2sinΘ=1 and sinΘ=1

sinΘ=1/2 and sinΘ=1

sin 30° sin 90° = π/2
sinΘ is + in Q1 and Q2,draw a diagram and reference angle of 30°

Q1 : Ref = Rel =π/6 OR 30°

Q2: π- π/6 = 5π/6

So answer of this equation is Θ = π/6 , π/2 , 5π/6

Note: If we need to calculator, make sure to set it to radians or degree .

Monday, September 19 - Solving Tirgonometric Equations on a SPecified Interval 1

What we did on the Monday class was a review of grade 11, just that we were solving with the 3 Special Triangles :

(they don't want to go in the right place)

How to solve for Ө:

1) Determine the reference angle
2)Select possible quadrant(s) using CAST rule,(Q1 Q2 Q3 Q4)
3)Check the interval given

4)State value(s) for Ө in degrees or radians.

Ex: 2SinӨ=1 interval 0-360

1st step: Solve for SinӨ
(I guess everyone knows how to solve this :P )
SinӨ= 1/2 = O/H (so we know its a 30* angle)

2nd step: draw a diagram (or not/or its given) and look in which quadrant it could be by using CAST rule, here we know it can be in Q1 and Q2 so we gonna get 2 equations

3rd step: calculate Ө in each possible quadrant(s) so Q1=ref. angle(now 30*)
Q2=180* - ref. angle (30*)
so we get the answers of Ө in Q1=30*
and in Q2=150*

Hope it is readable because my english is not so good :) ( in writing something down)

And Good Morning :P