[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]
