<span>[–2.5, –1.6):
Check the picture attached. The half closed interval of x, </span>[–2.5, –1.6) is shown with the red line segment.
The part of the graph corresponding to this interval is also shown. f(-2.5)<f(-2,4) so f (x) in not increasing in the first interval.
second interval, <span>[–2, –1]: in this interval, f(x) is decreasing.
</span>
(for larger values of x in this interval, the graphs decreases continuously, that is f(x) decreases.
third interval, <span>(–1.6, 0]:
The graph decreases for x from -1,6 up to a value close to -0.5. Then from this value to 0, the graph is constant.
So f(x) is not increasing.
the fourth interval </span><span>[0, 0.8):
This interval is shown by the purple line segment. Similar to the third case, in this interval for approximately half of the first values of x, f(x) is constant, then in the second half, f(x) is increasing.
</span><span>(0.8, 2)
in this interval, for larger x, we have larger f(x), so the function is increasing.
Answer: </span>(0.8, 2)
Check the picture attached. The half closed interval of x, </span>[–2.5, –1.6) is shown with the red line segment.
The part of the graph corresponding to this interval is also shown. f(-2.5)<f(-2,4) so f (x) in not increasing in the first interval.
second interval, <span>[–2, –1]: in this interval, f(x) is decreasing.
</span>
(for larger values of x in this interval, the graphs decreases continuously, that is f(x) decreases.
third interval, <span>(–1.6, 0]:
The graph decreases for x from -1,6 up to a value close to -0.5. Then from this value to 0, the graph is constant.
So f(x) is not increasing.
the fourth interval </span><span>[0, 0.8):
This interval is shown by the purple line segment. Similar to the third case, in this interval for approximately half of the first values of x, f(x) is constant, then in the second half, f(x) is increasing.
</span><span>(0.8, 2)
in this interval, for larger x, we have larger f(x), so the function is increasing.
Answer: </span>(0.8, 2)
