 # 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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Step 1
For $a,b\in \mathbb{R},a, real intervals are defined as follows:
$\left(a,b\right):=\left\{x\in \mathbb{R}\mid a
$\left(a,b\right]:=\left\{x\in \mathbb{R}\mid a
$\left[a,b\right):=\left\{x\in \mathbb{R}\mid a\le x
$\left[a,b\right]:=\left\{x\in \mathbb{R}\mid a\le x\le b\right\}$
Step 2
Each function is defined on domain. If the domain is a subset of $\mathbb{R}$ that contains intervals, you can ask which behavior the function has on these intervals.
For example, $f\left(x\right)={x}^{2},x\in \mathbb{R}$.
- is increasing on any interval (a,b), (a,b], [a,b), [a,b], $\left(a,\mathrm{\infty }\right)$, $\left[a,\mathrm{\infty }\right)$ with $a,b\in \mathbb{R}$, $a (these are all intervals an which f decreases).

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