The Function is increasing over the interval : -2 ≤ x ≤ 3
Proof : The Slope should be Positive over this Interval
Let us Calculate the Slope of the Function at which the Function is increasing.
We can notice that the Increasing Function part is passing through the Points (-2 , -3) and (3 , 3)
We know that Slope is given by :
[tex]\clubsuit\;Slope(m) = \frac{y_1 - y_2}{x_1 - x_2}[/tex]
⇒ [tex]Slope(m) = \frac{-3 - 3}{-2 - 3} = \frac{6}{5}[/tex]
As the Slope is Positive :
The Function is increasing over the interval : -2 ≤ x ≤ 3
