Question

Select the domain and the range for the graphed function below(4.)

Answer 1

Given:

The objective is to select the correct domain and range of the given graph.

Step-by-step 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.

`Domain\colon\text{ (-}\infty,+\infty)`

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.

`\text{Range: }(-\infty,3\rbrack`

Hence,

Domain: All real numbers.

Range: All real numbers ≤ 3.