image and pre-image of a function/interval

Hi,
I'm having a problem with setting the image of a function or interval of a function.
I do understand how to calculate the pre-image.
Example:
f(x) = -x^2 - 3

so to calculate the pre-image of the interval (0,1) I simply calculate 0 = -x^2 - 3 and I get minus square root of 3 and square root of 3,
and 1 = -x^2 - 3 and I get minus square root of 2 and square root of 2.

1) how to calculate the image of the function?
2)image of the interval (-1,3)?
3) and why is the pre-image of the interval (3,10) = 0 and (3,4) = http://upload.wikimedia.org/math/d/0...709b02e52e.png?

Thx

Quote:

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Originally Posted by misqa88

Example:
f(x) = -x^2 - 3
so to calculate the pre-image of the interval (0,1) I simply calculate 0 = -x^2 - 3 and I get minus square root of 3 and square root of 3,
and 1 = -x^2 - 3 and I get minus square root of 2 and square root of 2.
1) how to calculate the image of the function?
2)image of the interval (-1,3)?
3) and why is the pre-image of the interval (3,10) = 0 and (3,4) =

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I have read several of your post. I can suggest that you use a graphing calculator, a computer algebra or use this website.

Look long and hard at the graph. Then try to answer your questions.

The worst is I can read it from the graph but I don't know how to calculate it without one...
1) f= (-∞,3)
2) f(-1,3) = (-6,3)
I will have no time for drawing graphs for every single function on my test that's why I was looking for some help.
Thx