Question

Find the domain and range of the function graphed below. Domain: Range: ​

Answer 1

Domain: -1 ≤ x < 2

Range: 0 < y ≤ 4

Answer 2

Domain: [-1, 2)

Range: (0, 4]

Explanation:

Domain

The domain of a function is the set of all possible input values (x-values).

From observation of the graph, the x-values of the endpoints of the continuous curve are x = -1 and x = 2.

As there is a closed circle at endpoint (-1, 3), this indicates that x = -1 is included in the interval of the domain.

As there is an open circle at endpoint (2, 0), this indicates that x = 2 is not included in the interval of the domain.

When writing interval notation:

• ( or ) : Use parentheses to indicate that the value is excluded.
• [ or ] : Use square brackets to indicate that the value is included.

Therefore, the domain of the graphed function is:

• [-1, 2)

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Range

The range of a function is the set of all possible output values (y-values).

From observation of the graph, the highest y-value of the curve is y = 4 and the lowest is y = 0.

As there is an open circle at (2, 0), this indicates that y = 0 is not included in the interval of the range.

When writing interval notation:

• ( or ) : Use parentheses to indicate that the value is excluded.
• [ or ] : Use square brackets to indicate that the value is included.

Therefore, the range of the graphed function is:

• (0, 4]