Question

Use the graph to determine a a) open intervals on which the function is increasing if any b) open the intervals on which the function is decreasing if any and c) open interviews and which function is constant if any.

Answer 1

We are asked to determine open intervals on which the function is increasing, decreasing and constant.

a) open intervals on which the function is increasing if any.

As you can see from the graph, the function is increasing from x = 0 to x = 4.

So, the open interval in interval notation is

$increasing\colon\; (0,4)$

b) open the intervals on which the function is decreasing if any.

As you can see from the graph, there is no such interval where the function is decreasing.

The function is never decreasing.

c) open interviews and which function is constant if any.

As you can see from the graph, the function is constant from x = negative infinity to x = 0

So, the open interval in interval notation is

$constant\colon\; (-\infty,0)$

The function is also constant from x = 4 to x = positive infinity

$constant\colon\; (4,\infty)$

So, the overall interval is

$constant\colon\; (-\infty,0),\; (4,\infty)$