The I.O.I of y=x^2 is (0, infty), with the round brackets meaning that the value is excluded. Are there any scenarios where a square bracket would be used when stating the intervals of increase/ decrease for a function?

bsmart36 2022-08-11 Answered
Is a Square Bracket Used in Intervals of Increase/Decrease?
For example, the I.O.I of y = x 2 is (0,infinite), with the round brackets meaning that the value is excluded. Are there any scenarios where a square bracket would be used when stating the intervals of increase/ decrease for a function? If it narrows it down, the only functions I deal with are: linear, exponential, quadratic, root, reciprocal, sinusoidal, and absolute
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Answers (1)

Cynthia George
Answered 2022-08-12 Author has 10 answers
Step 1
For a , b R , a < b, real intervals are defined as follows:
( a , b ) := { x R a < x < b }
( a , b ] := { x R a < x b }
[ a , b ) := { x R a x < b }
[ a , b ] := { x R a x b }
Step 2
Each function is defined on domain. If the domain is a subset of R that contains intervals, you can ask which behavior the function has on these intervals.
For example, f ( x ) = x 2 , x R .
- is increasing on any interval (a,b), (a,b], [a,b), [a,b], ( a , ), [ a , ) with a , b R , a < b 0 (these are all intervals an which f decreases).

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