Given the function:
[tex]f(x)=(-x-1)^2+3[/tex]
As we can see, there is no restriction for x, it can be any real value. Additionally, looking at the graph, we do not see any discontinuity ("jumps" or "holes"). We conclude that the function is always continuous.
The vertex of the parabola is at (-1, 3), so x = 1 separates the intervals of increase and decrease. Going from -∞ to -1, we see a decrease in the y-values. Similarly, from -1 to +∞, we see an increment. Then:
Interval of increase: -1 < x < +∞
Interval of decrease: -∞ < x < -1
