What does a union in a function stand for??

Question

Hey everyone. I'm a freshman in Algebra II and I'm in a bit of a problem. I was doing some hw on domain and range of a function and I'm not really sure what the U is:
i.e.
f(x)=1/5x-7
D:(-infinity, -7/5)U(-7/5, infinity)

*All I want to know is what the union thing is for and when you use it.
*And why is -infinity part of the answer? My original answer was D: [-7/5,infinity).
*What would you do to find the range? I know how to get the range in quadratic functions, but the 1/5x-7 confuses me. Thanks so much.

I know these are a lot of questions, but I just don't get Algebra! Geometry was more my thing...

Answer 1

The U is set notation for the union of two sets and replaces the word "or" in English. In your case,

(-infinity,-7/5) U (-7/5, infinity) is the same as

x < -7/5 or x > -7/5. I don't know why it is expressed this way because this simply means x is any real number except -7/5.

Since f(x) = y = 1/(5x - 7), we can solve for x to help us get the range. Remember, the range are the possible y values and the domain are the possible x values

So, y(5x -7) = 1
5xy - 7y = 1
5xy = 7y + 1
x = (7y + 1)/5y.

Now, x will be undefined if y = 0. Therefore, the range is any real number except y. You could write it in set notation as follows:

R = (-infinity, 0) U (0, infinity) which simply says y < 0 or y > 0

Hope this helps

Answer 2

Oh man, you just made me so glad I"m out of school! :-)

Answer 3

i have no idea i'm just about to go to geomotry. i don't know. sorry dude(et)