Answer: D: x ∈ [0, 4)
Explanation:
For a function:
y = f(x)
The range is the set of the outputs, the possible "y" values
The domain is the set of the inputs, the possible "x" values.
Now, we want to see the domain in which the function increases.
First, we can see that the whole domain of the graph is the interval:
[0, 9]
And a function is increasing if, reading from left to righ, the graph goes upwards.
In the image, we can see that the graph increases in the segment:
[0, 4)
Where we have an open segment because in the point x = 4 the graph stops increasing.
Then the domain where the function increases is:
D: x ∈ [0, 4)