Find the range of function f(x)=1/x, x<0
- Thread starter ickw
- Start date
Because [MATH](a,\ b)[/MATH] EXCLUDES both a and b.
More interesting to me is why you thought dividing 1 by a negative number could generate a positive fraction or 1 itself.
Moreover, your proposed range includes zero. What number do you divide a number by to get a quotient of zero?
I am really glad you asked this question because I think it will make you review your understanding of interval notation, which may save your bacon on a test.
More interesting to me is why you thought dividing 1 by a negative number could generate a positive fraction or 1 itself.
Moreover, your proposed range includes zero. What number do you divide a number by to get a quotient of zero?
I am really glad you asked this question because I think it will make you review your understanding of interval notation, which may save your bacon on a test.
Dr.Peterson
Elite Member
- Joined
- Nov 12, 2017
- Messages
- 16,088
Another helpful question would be, how did you come up with (-∞,1]? There may be some additional issues to be dealt with after you explain your thinking.
HallsofIvy
Elite Member
- Joined
- Jan 27, 2012
- Messages
- 7,763
\(\displaystyle (-\infty, 0)\) does NOT include 0 but does include every negative number up to 0.
And do NOT ever say of yourself that you are dumb. There will be too many other people willing to do that for you!
And do NOT ever say of yourself that you are dumb. There will be too many other people willing to do that for you!
Dr.Peterson
Elite Member
- Joined
- Nov 12, 2017
- Messages
- 16,088
It is a common mistake when students first see this sort of thing, to focus on integers and think that the numbers less than 0 are just -1, -2, -3, ... . That often happens because the student graphs specific points, rather than imagining the continuous graph, which is a new concept. Changing your perspective just takes a little experience. And your realization is that experience!
So, as Halls said, you aren't dumb, just not at the goal yet. (That's what education is for -- to get you there, in your own time!)