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Thursday, February 23, 2006

LUCKY SCRIBE # 13?!?!?!?!!!!




(un)LUCKY SCRIBE # 13,JEFFERSON REPORTING FOR DUTY!!!! Hiya. Today we had only one precal class today and today's lesson was quite, how you say,enjoyable. The fi rst half of the class, Mr k gave a brief explanations on the difference of functions and relations(gr 11). A function has one y value for every x value, however a relation has one x value for different y values. A function passes the vertical line test while a relation does not


He then explain that there2 kinds of functions or "flavors as how Mr K put it. One "flavour"(strawberry) has many(more than one) outputs for one input(2:1 function). For example:
y = x^2
f(-2) and f(2) = output of 4 there fore the out put is 4

The other "flavor(rocky road) has one input for one output. A 1:1 relation would be

y=x

Each input has its own output. Not every function has it's own inverse.

relations have many inputs for one output. Now here's the my favorite part where I understood what was happening. y = x has its own inverse ITSELF. Meaning the inverse doesn't look like it changed at all. I mean no coordinates or flips. Examples of theses are: y = cube root(x) and y = square root(x). If you want to see what the graph looks like, you can punch in the equation on the calculator.

Mr K then gave us notes to add into our math dictionary.(this will probably clear things for you and make it easier to understand)


Inverses: The inverse of any function f(x) is written as f^-1(x)


IMPORTANT!!!!!


F^-1(x) is read as : ”f inverse”
F^-1(x) “undoes” what ever f does


Example





Notice that the domain and range of a function becomes the range and domain respectively in the inverse


Numerically:


Given any ordered pair (a, b) from a function f, the inverse is found by exchanging the coordinates (b, a) in a table of values we simply Exchange the inputs and outputs.


Example




Symbolic(as equation)
To find the inverse of any function exchange the variable x and y, then solve for y (sqr = square root)
Algebraically:
y = (2x-3)^2
x = (2y-3)^2
sqr(x) = 2y - 3
sqr (x) + 3 = 2y
Sqr (x)/2 + 3 /2 = y
*note y = (2x-3)^2 and Sqr (x)/2 + 3 /2 = y are inverses


Conseptually:
We use the operations in a given function then write a second list, in reverse order of the inverse operations


Example:


f(x) = cube root(x^2 - 3)/2

1.square
2.subtract 3
3.cube root

4.divide by 2


f^-6
1.multiply by 2
2.cube
3.add 3
4.square root
F^-1(x) = sqr ( (2x)^3 +3)

F^-1(x) = sqr ( (2x)^# +3)
Graphically:


Given the graph of any function f we can find the inverse graph, f^-1 by reflecting f in the line y = x
Example: (solid blue line = line of reflection)

phew...that took me about 3 hrs on this scribe. It took my one hour for drawing the diagrams and 2 hrs typing up the math dictionary and read my mess of notes from Mr K's lecture and making the blog post nice and colourful =). I feel proud of myself because i've done one what looks like a good job from my perspective.Any ways its time for me to go STUDY HARD FELLOW STUDENTS!! REMEMBER WE WANT TO BE IN THE 80%+ RANGE!!

"MAY THE UNIT CIRCLE BE WITH YOU"

later days, Jefferson

OH YEAH. the scribe I pick next is the one who sits at the other end of the classroom, who? its Anh!!!!!




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1 Comments:

At 3/01/2006 3:09 PM, Blogger Regine said...

yep. I think you did a heck of a job, Jeeferson. haha. It does take SO long to make just one scribe. Mann. but yours looks good and it's understandable. *thumbs up*

 

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