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Rob: The following is taken from the textbook: "Calculus", by Ross
Finney and George Thomas Jr., published by Addison Wesley, the
most understandable book on the subject I have found so far.
I. Definitions:
A.The domains and ranges of many functions are intervals of
REAL numbers.
1) The set of all real numbers that that lie
STRICTLY BETWEEN two Fixed numbers a and b is an
OPEN interval. It is open at each end because the set
contains neither of its endpoints. Ie:
(a)<=========================>(b) [OPEN]
a < x < b
2) Intervals that CONTAIN both end points are CLOSED.
<(a)========================(b)> [CLOSED]
a <or= x <or= b
3) Intervals that contain One but Not Both end points
are HALF OPEN, but you get the point.
a < x <or= b (for example).
B. The domains and ranges of functions can also be
INFINITE intervals:
1) The set of all real numbers (- infinity, + infinity) :
- Infinity<============ 0 =================>+Infinity
-infinity< x <+infinity, where x=0.
(In our definition there is no number called infinity.)
2) The set of numbers greater than a: (a, infinity)
------------------- a============x>+ infinity
a < x < infinity
3) The set of numbers greater than or equal to a:
-------------------a=================x>+infinity
a <or= x
4) The set of numbers less than b: (- infinity, b)
-infinity<x============b-------------------
-infinity<x<b
5) The set of numbers less than or equal to b: (-infinity,b)
-infinity<x=============b------------------
-infinity<x<or=b
C. EXAMPLES:
In each of the following functions, the domain
is the largest set of values for a Real X input and a Real Y
output.
Function Domain Range
------------------------------------------------------------------------
Y=X^2 - INFINITY< X < + INFINITY 0 <or= Y
Y=(1-X^2)^1/.2 -1<or=x<or=1 0<or=y<or=1
Y=1/X X<>0 Y<>0
Y=(4-X)^1/2 X<or= 4 0<or= Y
Note: x<or=y: (x is less than or equal to y)
X^2: (X squared)
X^1/2 : (Square root of X)
I hope this helps! (The KsKid)
posted by 24.22...
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