|
Question 207876: My name is Sara, I need help really bad.
Can someone describe what the graph of interval [-4,10] looks like?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the short answer to your question is as follows:
-----
the interval [-4,10] means -4 <= x <= 10
-----
x represents any number that is within your interval. x can be -4 and it can be 10 and it can be any number in between.
-----
another way of showing this is:
x >= -4 and x <= 10
-----
interval notation and the graph of an interval are related.
the graph of the interval is a pictorial representation of the interval notation.
-----
the graph of your interval would be the number line that you should be familiar with.
-----
you can find a picture of your interval at the following website:
http://theo.x10hosting.com/
-----
click on problem number 207876
-----
different persons describing the graph of an interval will use different symbols to represent greater than, less than, greater than or equal to, less than or equal to.
-----
the general form of the interval is a,b
a is the smallest number of the interval
b is the largest number of the interval
-----
my notation is as follows:
-----
(a,b) means your interval is from a to b but does NOT include a and does not include b.
in algebraic notation this would be a < x < b.
this means that a is less than x and x is less than b.
another interpretation is that x > a and x < b.
this means that x is greater than a and x is less than b.
-----
[a,b] means your interval is from a to b and DOES include a and b.
in algebraic notation this would be a <= x <= b.
this means that a is less than or equal to x and x is less than or equal to b.
another interpretation is that x >=a and x >= b.
this means that x is greater than or equal to a and x is less than or equal to b.
-----
you can mix and match.
if you want to show that x > a and x <= b, you would show as follows:
(a,b]
-----
if you just want to show that x > a, you would show as follows:
(a, )
this means that a < x <
this also means that x > a and x <
-----
if you just want to show that x <= b, you would show as follows:
( ,b]
this means that < x <= b
-----
there is also the concept of union of intervals which ties two disjointed intervals together. i will show you what that looks like on the picture also.
-----
an example of that would be:
x < 2 or x >= 6
in interval notation this would look like:
(,2) union [6,)
-----
you can never be greater than or equal to minus infinity.
you can never be less than or equal to infinity.
you can only be greater than - infinity.
you can only be less than infinity.
-----
some websites that have additional information that can help you are shown below:
-----
describes interval notation:
http://id.mind.net/~zona/mmts/miscellaneousMath/intervalNotation/intervalNotation.html
-----
has some practice problems for you to test your knowledge on intervals and shows them in interval graph form:
http://www.regentsprep.org/Regents/math/ALGEBRA/AP1/IntPrac.htm
-----
contains interval notation and graph of interval notation:
http://www.regentsprep.org/Regents/math/ALGEBRA/AP1/IntervalNot.htm
-----
is talking about solving linear inequalities but in the process is showing what it looks like on an interval graph. forget the problems and just go to the interval graphs and what they represent. covers all combinations you might need. don't let the equations throw you. it's the graph and the interval notation that has already been solved that you are looking for.
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut22_linineq.htm
-----
my short course:
-----
(-4,10)
x is greater than -4 and x is less than 10:
-4 < x < 10
-----
THIS ONE REPRESENTS YOUR PROBLEM:
[-4,10]
x is greater than or equal to -4 and x is less than or equal to 10:
-4 <= x <= 10
-----
(-4,10]
x is greater than -4 and x is less than or equal to 10:
-4 < x <= 10
-----
[-4,10)
x is greater than or equal to -4 and x is less than 10:
-4 <= x < 10
-----
don't forget the picture of the graph of your interval on the website.
-----
-----
you can find a picture of your interval at the following website:
http://theo.x10hosting.com/
-----
click on problem number 207876
-----
|
|
|
| |
