Given:
The objective is to select the correct domain and range of the given graph.
Explanation:
To find domain:
Domain is defined as all the possible values of x in the graph. By observing the graph, the end points are continuing all the way from negative x-axis to positive x-axis.
Then, the domain of the graph will be all real numbers.
[tex]Domain\colon\text{ (-}\infty,+\infty)[/tex]
To find range:
The range is defined as the all possible values of y in the graph.
By considering the graph, the vertex lies on the coordinates (-3,3).
For a parabolic graph,
If a < 0, the range will be y ≤ 3.
If a > 0, the range will be y ≥ 3.
Since, the parabolic graph is open downwards then a must be less than zero.
Thus, the range of the graph will be all real numbers less than or equal to 3.
[tex]\text{Range: }(-\infty,3\rbrack[/tex]
Hence,
Domain: All real numbers.
Range: All real numbers ≤ 3.
