Question

The function f(x) is graphed. In two or more complete sentences, describe how to find the interval(s) where the function is increasing and how interval notation is used to express the interval(s). In your final answer, include the interval in which the function is increasing.

Answer 1

If the slope of a line segment is positive, it is increasing over that segment.
In the given graph, it is increasing over (-5,0].

Answer 2

Answer with explanation:

In the given graph, the graph started increases( from left to right )after x=-5 which is represented by an open circle(o)  i.e. x=-5 is not an included point.

Also, the graphs continues to increase until it has reached a point at x= 0 which is  represented by an closed circle  i.e. x=0 is an included point.

i.e. for -5 <x ≤0 , function f(x) is increasing.

In interval notation : (-5,0]        

[We use open bracket () to show not included point and closed bracket [ ] to show included point]

Hence, the function is increasing for all $x\ \varepsilon (-5,0]$