Answer:
Domain: (-∞, 3]
Range: (-∞, 3]
Step-by-step explanation:
Domain
The domain of a function is the set of all possible input values (x-values) for which the function is defined.
The right endpoint of the graphed function is a solid circle at the point (3, -4). A solid circle at an endpoint indicates that this value is included in both the domain and range.
The left endpoint of the graphed function is an arrow, indicating that the function continues indefinitely in that direction. This means there is no finite left endpoint, and the function values continue without bound as x decreases.
Therefore, the domain includes all real numbers less than or equal to 3. In interval notation, this is expressed as:
[tex]\LARGE\boxed{\boxed{\textsf{Domain:} \;\;(-\infty, 3]}}[/tex]
We use ( to indicate that the left endpoint is not included (because it extends indefinitely to the left), and ] to indicate that the right endpoint is included (because it's specified as part of the function).
[tex]\dotfill[/tex]
Range
The range of a function is the set of all possible output values (y-values) for which the function is defined.
The maximum value of the graphed function occurs when y = 3, and the function extends indefinitely towards negative infinity as x decreases.
Therefore, the range includes all real numbers less than or equal to 3. In interval notation, this is expressed as:
[tex]\LARGE\boxed{\boxed{\textsf{Range:} \;\;(-\infty, 3]}}[/tex]
We use ( to indicate that the minimum value is not included (because it extends indefinitely towards negative infinity), and ] to indicate that the maximum value is included in the range.
