Creating Equations for Sinusoidal Functions

Hi! This is kyle and we learned about how to create equations for sinusoidal functions.

So, these are the things that you need to know first..
a - amplitude
b - |b|
c - horizontal shift
d - vertical shift
because those are the ones the will be going to be plugged in f(x) = a sin b(x - c) + d or f(x) = a cos b(x - c) + d

moving on..

STEPS ON FINDING THE EQUATION FOR SINUSOIDAL FUNCTIONS:
1.) Find the middle axis (d - vertical shift) of the graph. It is the one that determines the up and down shifting of the graph.
2.) Determine the amplitude.
3.) Determine the period. Then, you can now solve for the |b| value.
4.) Identify the type of wave. It is only either sin or cos.
5.) Determine the horizontal shift by counting how many radians it shifted to the left or right.
6.) Create the equation by plugging the a,b,c,d value in f(x) = a sin b(x - c) + d or f(x) = a cos b(x - c) + d

Absolute Value Function

Hello fellow classmates! This is Paulene :D Yesterday, we learned what an Absolute Value Function is and how to graph it.

This is the Parent Graph of all absolute value functions or "Basic Shape" f(x) = |x|

It has the same V-shape, but they can be wider or narrower. They might have their vertex somewhere else other than the origin, and they might open downward instead of upward.



Shifted Shape: f(x) = |x-h| + k :: You read k as is and h as opposite.

How to graph by "reading" an Absolute Value function:
1. Read k values as is. If k is positive, the graph shifts up.
If k is negative, the graph shifts down.
2. Read h values as opposite. If h is positive, the graph shifts left.
If h is negative, the graph shifts right.

Eg. (f)x = |x+1| + 2 :: The graph will shift 2 up, 1 to the left.

How to graph an Absolute Value Function using a table:

1. Choose an x-value
2. Sub in the value for x in the equation
3. Simplify
4. The answer is the now the y-value
5. Repeat Steps 1-4 for 2-4 more x-values and sketch the function.

Eg. (f)x = |x+2|

x value - y value

0 - |0+2| = 2
1 - |1+2| = 3
2 - |2+2| = 4
-1 - |-1+2| = 3
-2 - |-2+2| = 0

Reciprocal Functions 2

Hi guys! Last Thursday we learned How to Graph Reciprocal Trigonometric Functions.

How to graph:

• ( when period is )

1. Graph the basic sin x shape.

2. Place vertical asymptotes in x-intercept where reciprocated sin x is undefined ( 0, , )

3. Flip the remaining curves.

• (when the period is )

1. Graph the basic cos x shape.

2. Place vertical asymptotes where reciprocated cos x is undefined ( , )

3. Flip the remaining curves.

• ( when period is )

1. Create a table of values using quadrantals and 's ( refer to booklet )

2. Since , place vertical asymptotes on 0, , .

Reciprocal Function

Hi! Paul here. Yesterday's lesson was about Reciprocal Function. We learned it from grade 11 and yesterday was like a review so I made a little something for this topic. Click here. It shouldn't be that hard because we only had the basics yesterday. All we need to do is to find the asymptotes then graph the reciprocal function (use table of values because the numerator isn't always going to be 1). That's all. Don't forget to check the link up there. ^ ;)

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.