CAA: Christian Anime Alliance

I don't understand one lick of it. It's just way too confusing. The SAT book's explanation (or lack of) was far to sparse for me to grasp. And I can't seem to find a site that is both thorough and to the point. After all, I don't have time to reinvent the wheel. I'm out of school, and my SAT test is this Saturday, and I don't understand functions.

But if anyone could point me in the direction of a veeerrry good explain. I mean an explanation so good that an elementary kid could understand, I would looove you!

After all, it's not a matter of what part don't I understand, I don't understand ANY of it.

What are you required to know about functions? That might affect the depth and breadth of any explanations. In terms of the basic defintion, a function is any operation on a variable x such that for any given value of x there is only one resulting output of the operation.

In other words, given some value x, a function of x is an operation f(x) such that the outcome y=f(x) is unique. For example:

f(x)=x^2 is a function since for any value of x there is a unique value for the result.

f(x)=sqrt(x) is not a function as it is defined here, since the result of any operation on x is not unique. e.g. sqrt(4)=+2 or -2.

f(x)=sin(x) is a function since there is only one possible result for a given value of x.

The domain of a function is the set of permissible values of x. For example:
the domain of f(x)=x^2 is all of the real number line.

the domain of 1/x is all of the real number except for x=0.


The range of a function is set of all possible values of f(x) given the domain.
For example, the range of f(x)=x^2 is the set of all real numbers greater than or equal to zero (ignoring complex values for x for the time being.)

You could also try the following explanation:
http://mathworld.wolfram.com/Function.html

To save a bit of clicking, a one to one function means that not only is the value of the function unique for that value of x, but that that value of x is the only one that will give that result.

Thanks. I think hat helped a bit. Now my issue is here since I'm at loss for this part.

Where the heck did g(x+3) come from in the example on 261 (the written part, not the graph)?

And for page 262 why is the choice E and not B. How can x-1 shift right? I must not be on the same wave here since I don't get the logic of functions very well at all.

Page 261 is simply a case of bad wording. What they are try to say is that you should be able to calculate and identify functions that have been shifted in their independant variable (i.e. x). In this case, the author has chosen to g(x) to be a generic concept, and f(x) to be a specific example of a problem.

On page 262, you are given multiple choices for the plot of f(x-1). Remember, that this is a shift in x. We can calculate the original function f(x) as

{f(0)=1, f(1)=2, f(2)=1, f(3)=0, f(4)=-1}

where f(x) is undefined for x<0.

The above list is derived from simple observation.

Therefore: f(x-1)=
{ f(1-1)=1, f(2-1)=2, f(3-1)=1, f(4-1)=0, f(5-1)=-1}

Inspection will reveal that this corresponds to a right shift of the entire function.

TM, when I read that last sentence, I imagined you with a british accent, and I was like, "what kind of shift..."

Well, it's been a right hard day...

Thanks.