Question

How do you find range of a function?

Answer 1

For example, \[1\div(x^3-x)\], the domain is all real values of x except 0, +1 and - 1. What do you do for the range though?

Answer 2

y can't equal zero

Answer 3

That answer is correct, but how did you get to that?

Answer 4

in this question you need to solve x^3 - x = 0.... this will give the restictions in the domain

and these values will also be vertical asymptotes.

the range will be all real y except y cannot = 0 as the numerator of the expression is the constant 1.

there is a horizontal asymptote at y = 0

Answer 5

So if there is a constant in the numerator, we can assume that there is an asymptote at y = 0?

Answer 6

yeah

Answer 7

That makes sense because you'll never get zero as an output.

Answer 8

I'm having fun re-learning all of this stuff :-)

Answer 9

So whenever we have something over a huge polynomial where we might have absolutely no idea what the function is going to look like, there will be asymptotes at any of the "zeros" we find for x.

Answer 10

right?

Answer 11

thats correct... and oblique asymptotes can be found by polynomial division... and don't worry about the remainder

Answer 12

@Luis Rivera you are absolutely right

Answer 13

Thanks @campbell_st this is starting to become clearer.

Answer 14

Hey you guys, google this one: graph (x+2)/(x^9+1)

Answer 15

Well the domain would be anything except -1, but I still not sure how to find it's range
:S

Answer 16

vertical asymptote at x = -1

Answer 17

Strange how it droops like that...

Anyway, I'll quit wasting time lol

Answer 18

horizontal asymptote at y = 0

Answer 19

Now we need to start evaluating some R3 functions ;-)

Answer 20

How did you find the horizontal asymptote for that function?