This present day we got straight to the point, and we began our second quiz on Transformations! woo.

20 minutes go by...

Sweat dripping on papers, palm's moist, and mouth's dry from the intensifying surge of power radiating from our quiz sheets. "Time's up! Time's up! Time's up!" yells Mr. Kuropatwa. Thirty sweat, and acne filled faces look up at the clapping hands of Mr. K as he commands us to advance our papers to the front of the classroom.

And so the alteration of our papers begin:

Odd Function: Symmetric with respect to the origin

Average-Minded Definition of an Odd Function: If you rotate the graph of the function 180 degrees: it'll be the same

We are told that this function is an Odd Function, ergo we must complete it.

This is the completed graph. woo.

Now let's put it to the test!...

Would you look at that! I have rotated the graph 180 degrees, and it looks completely identical!

Next question...

Graph the Reciprocal of the function.

Facts we know:

- Vertical Asymptote is where y= 0 because the reciprocal of the point is undefined
- The In-variant (unchanging) points are where y= 1, and where y= -1
- Class is long

Dotted Blue Line: Vertical asymptote, where y= 0

Yellow Points: In-variant points, where y= 1, and y= -1

Green Line: Reciprocal of the horizontal line coordinates (x= 2 - 4 , y= 3)

Next Question...

Next we are asked to sketch the graph of f(x) = 1 /| x-2|

To answer this question, we must first find the graph of f(x) = |x+2|

BUT BEFORE we find the graph of f(x) = |x+2|, we MUST first find the graph of

f(x) = x-2

Red Dot: -2 is a y-coordinate of the line

Blue Dot: Slope of the line is (rise/run) in this case it's (1/1); moving up once from -2, and moving to the right once ending in coordinates (x= 1 , y = -1)

To turn it into |x-2| : all negative coordinates turn positive:

To find the reciprocal of the function we use the

Facts We Know:

- Vertical Asymptote is where y= 0 because the reciprocal of the point is undefined
- The In-variant (unchanging) points are where y= 1, and where y= -1
- And yes class is long

Final Question...

With the function y= x , we are to expand it vertically by a factor of 2, shift it 3 units to the left, and take its reciprocal. With this new function we are asked to write a new equation for it, and sketch it on a graph.

First we'll write the Equation:

y = x

The first thing the question asks us to do is to expand the function vertically by a factor of 2. We accomplish that by writing

f(x) = 2x

Afterwards we must shift the function 3 units to the left, so the equation becomes:

f(x) = 2(x+3)

Finally we take it's reciprocal which is basically flipping it, switching the numerator, and the denominator's positions.

f(x) = 1/[2(x+3)]

or

f(x) = 1/(2x+6)

With this new equation; we can sketch the graph to this new function derived from y = x.

To sketch this function we must first sketch f(x) = 2x+6

6 - y-coordinate of function

2/1 - slope of function

Now we take the reciprocal of the function with our FACTS

- Vertical Asymptote is where y= 0 because the reciprocal of the point is undefined
- The In-variant (unchanging) points are where y= 1, and where y= -1

And there you have it a sketch of the new function.

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It's been fun, I love spending my Wednesday mornings (2am) working on math stuff. Anyways here's a joke I have been holding in every time Mr.K asks us if we had any good jokes.

woo! Here it is:

An anion was walking down the street, and he saw a cation. The cation was looking pretty sad, so the anion went up to him, and asked him if anything was wrong. The cation looked at him and told him he had lost an electron. The anion asked him, "Are you sure?" and the cation said, "I'm positive!"

*Thanks Jasmin for refreshing that for me*

Hopefully you all understood that, I'm hoping.

SO, onto the juicy part that everyone skips to, and misses everything i wrote to check if they're the scribe post for the next day... muahaha time to put a frown on someone's face.

My buddy!! JOE S!! Your next, put down your psp.

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