Explanation
Here the question wants to find the range of function. Your answer is incorrect because you are confusing between range and domain.
Domain is the set of all x-values. That means any values that are part of x are subset of domain itself. We can find domain two ways which are
- Relation method
- Graph method
But we are not talking about domain as we are looking for the range of function.
Range is the set of all y-values. In the relations or ordered pairs (x, y). Our y is the range. Range can also be called Co-Domain or Output. But of course, we are not talking about finding range using relation method. We are going to find range by looking at the graph.
The range starts from minimum value to maximum value. If there is another point between minimum value and maximum, just ignore it.
Here is a diagram or easier way to understand.
[tex] \boxed{minimum} \Longrightarrow \boxed{maximum}[/tex]
From the graph, our minimum is -5 and our maximum is -1. Notice that there is another opened point at -2 which we are supposed to ignore. Because both minimum and maximum are closed dots. Hence, we use >= or <= only.
Therefore the solution should be
[tex] - 5 \leqslant y \leqslant - 1[/tex]
Answer
[tex] - 5 \leqslant y \leqslant - 1[/tex]
