Answer:
A closed circle on the graph indicates that the point is included in domain and range. An open circle indicates that the point is not included in the domain and range.
Now based on this, we will evaluate the given options:
Option A. The function g(x) is defined for all real numbers x.
The lines on the graph contain a limited values. Hence its obvious that the domain and range is not the set of all Real numbers. Hence this option is Wrong.
Option B. The maximum value of the range is 4.
From the graph we can see that the maximum/highest value along y-axis is 4. Since there is a closed circle at (-4, 4), this value is included in the range. Hence this option is True.
Option C. The maximum value of the domain is 3
There is an open circle at the point when x is 3. Hence this point is not included in the Domain. Value of domain is numbers less than 3. Hence this option is Wrong.
Next two options are incomplete. Here are the complete options and listed correctly.
Option D. The range of g(x) is {yl -1 < y ≤ 4}
This is correct because there is an open circle at point (3, -1). Hence -1 would not be included in the range. The range will be set of all values from -1 to 4, including 4 as there is a closed circle at (-4, 4)
Option E. The domain of g(x) is {x| x ≤ -4 ≤ -1 or 0 ≤ x <3}
Since there are closed circles at points where x is -4, -1 and 0, these points would be included in the Domain. 3 wont be included in the Domain as there is an open circle.
