### 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 : Âf inverseÂ

F^-1(x) ÂundoesÂ 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)

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!!!!!

## 1 Comments:

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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