The function f(x) from the graph f'(x)

1. The function is increasing at (-2,0) and (0,2)
The function is decreasing at (-∞,-2) and (2,∞)
You can tell because at these intervals the outputs are the same as the slope of f(x). Increasing means the slope is positive and decreasing means the slope is negative.

2. There are possible extrema at the points x=-2, x=0, x=2 because at those points the output is zero.

3. At (-1,0) and (1,-∞) f(x) is concave down and at (-∞,1) and (0,1) f(x) is concave up because the slope of f'(x) is negative @ (-1,0) and (1,-∞) and positive @ (-∞,1) and (0,1).

4.The function is possibly either f(x)=sinx or f(x)=cosx.

Pokemon and Calculus

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LOL

Limits Suck!!

I do sort of understand the concept behind limits but there is still ALOT of things that confuse me..... here are just the 3 most confusing:

1) How the heck do you figure out a limit approaching infinity without knowing what the graph looks like?!!!!!

2) What do you do when you can't plug in a limit because you get undefined but you can't simplify the equation to remove the problem.

3) Whats the difference between finding continuity and discontinuity?

Tips and Hints

1) I remember transformation mostly by looking for the parent function of a given function. To graph it, i start by drawing a sketch of the parent function. From there i look at what has been done to the original function and make me transformations accordingly.

2) Basically all that i know about trigonometry is down to the unit circle. Admittedly though, trig. is my most trouble concept. Something helpful to me to remember the ordered pairs on the unit circle is starting from pi over 3, count 1.... 2.... 3.... for all the x's, then count 3....2....1...... for all the y's. then put square root on all the numbers expect the one's and put everything over 2.

3)What ABSOLUTELY confuses me in trig its how to apply transformations to all the trig. functions. I need MOST help on that!!!

Logs and Inverses

What I Understood:
In a logarithmic function, when one gives an input, it will output the exponenent of the given base. For example, if one input 8 into log base 2 the output will be 3.

To find out if the inverse of a function is possible, one may use the horizantol line test the same way one uses the vertical line test to determine of a graph is a function.

The inverse of a fucntion, wether it is a fucntion or not, is mirrored about the line y=x. This makes graphing the inverse of a graph much easier.

The inverse of in exponent is a logarithm.

Misunderstood:
how to solve a piece wise function with a log

how to apply transformtion of a log function

Even and Odd Functions

In graphical terms an even function looks like this:

An even function is symmetrical with respect to the y-axis.

An odd function looks like this

An odd function is symmetrical with respect to the orgin (0,0)


These graphs are exactly the same as saying an even function is f(-x) = f(x) and an odd function is f(-x) = -f(x).


Even Function:
This is so because for any function of f(x),when you alter the input (x) the graph of the function transforms. In this case when the input is made negative, the image of the graph is mirrored. Therefor for, if a graph that is symmetrical about the y-axis is transformed into f(-x) it will be exactly the same as the orginal function.


Odd Function:

CALCULUS FAIL!!

AHH!! Calculus is scaring me!!! I forgot a lot of things!!!
I think I am going to end up answering things like this:


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