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Identify intervals on which the function is (a) increasing, (b) decreasing, and (c) constant. In each case, assume that the domain of the function is (-∞, ∞) and that any characteristics of the graph continue as indicated.

Identify Intervals On Which The Function Is A Increasing B Decreasing And C Constant In Each Case Assume That The Domain Of The Function Is And That Any Charact class=

Sagot :

[tex]\begin{gathered} (-\infty,1\rbrack,decreasing \\ (1,\infty)increasing \end{gathered}[/tex]

1) In this question, we need to remind ourselves of the definition of an increasing or decreasing interval.

2) When the function is increasing we have:

[tex]x_2>x_1,f(x_2)>f(x_1)[/tex]

On the other hand, a given interval of a function is decreasing when:

[tex]x_2>x_1,f(x_2)3) Examining the graph we see two intervals:[tex]\begin{gathered} (-\infty,1\rbrack \\ (1,\infty) \end{gathered}[/tex]

Note that for the first interval the more the f(x) values increase the x values decrease.

So,

[tex]\begin{gathered} (-\infty,1\rbrack,decreasing \\ \end{gathered}[/tex]

And on the other hand, the more the x values increase the more the f(x) values increase, so:

[tex](1,\infty)increasing[/tex]

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