INTERVAL NOTATION

[plac6636]

I'M REALLY CONFUSED ON HOW TO WRITE A FUNCTION'S DOMAIN AND/OR RANGE IN INTERVAL NOTATION. IF YOU HAVE A PARABULA THAT OPEN UPWARD W/THE BOTTOM POINT AT (0, -4) I KNOW THAT THE DOMAIN IS {X\ ALL REAL NUMBERS} OR (-"INFINITY", "INFINITY") AND THE RANGE IS {Y\ Y > -4} BUT WHAT ARE SOME HINTS ON WRITING THAT IN INTERVAL NOTATION?

 

[pka]

{y| y≥a}=[a,∞).
{y| y>a}=(a,∞).
{y| y≤b}=(−∞,b].
{y| y<b}=(−∞,b).
{y| a<y<b}=(a,b).
{y| a<y≤b}=(a,b].
{y| a≤y<b}=[a,b).
{y| a≤y≤b}=[a,b].

 

[plac6636]

SO IF YOU ARE ASKED TO GIVE AN ANSWER FOR DOMAIN IN INTERVAL NOTATION, WOULD IT GO ALONG WITH THE SAME GUIDES THAT YOU GAVE ME FOR RANGE?

 

[stapel]

Yes, except that you'd probably use "x" instead of "y".

Eliz.

 

[pka]

Yes. The point being that interval notation is about the way we write connected subsets of real numbers.
They are used for domain, range, solution sets, and more.
I gave you the complete list of the eight possible intervals.

{x| x≥2}={y| y≥2}={Θ| Θ≥2}=[2,∞).
It is just notation for sets of real numbers.
If the domain is the set of reals at least −5 and less that 6, write [−5,6).
If the range is all reals greater that 1, write (1,∞).
The solution set for |x−3|≤2 is written in interval notation as [1,5].