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

Question

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

Cynthia George · Accepted Answer

Step 1For   a  ,  b  ∈      R    ,  a  &amp;lt;  b, real intervals are defined as follows:  (  a  ,  b  )  :=  {  x  ∈      R    ∣  a  &amp;lt;  x  &amp;lt;  b  }  (  a  ,  b  ]  :=  {  x  ∈      R    ∣  a  &amp;lt;  x  ≤  b  }  [  a  ,  b  )  :=  {  x  ∈      R    ∣  a  ≤  x  &amp;lt;  b  }  [  a  ,  b  ]  :=  {  x  ∈      R    ∣  a  ≤  x  ≤  b  }Step 2Each 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  &amp;lt;  b  ≤  0 (these are all intervals an which f decreases).

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?

Answered question

Answer & Explanation

New Questions in Integral Calculus