Question

NO LINKS!! State the Domain and Range for each graph​

Answer 1

1. Domain: [-2, 6]

Range: [-3, 7]

2. Domain: (-∞, ∞)

Range: [1, 5]

Explanation:

Definitions

• Domain: The set of all possible input values (x-values).
• Range: The set of all possible output values (y-values).
• Open circle: The value is not included in the interval.
• Closed circle: The value is included in the interval.
• Arrow: The function continues indefinitely in that direction.

Note: Assume that each square on the given graphs is 1 unit.

Question 1

The domain of the function is restricted since the curve has two distince endpoints. As each endpoint is marked by a closed circle, the x-value of the endpoints is included in the domain.

• Domain: [-2, 6]

The function has a maximum point at (-1, 7) and a minimum point at (6, -3).

Therefore, the range of the function is restricted.

• Range: [-3, 7]

Question 2

As there are arrows at both endpoints of the function, and the function is continuous between the arrowheads, the domain is unrestricted.

• Domain: (-∞, ∞)

The maximum y-value is y = 5. When x < 1, the line continues indefinitely at y = 5.

The minimum value is y = 1. When x > 1, the line continues indefinitely at y = 1.

Therefore, the range of the function is restricted.

• Range: [1, 5]

Answer 2

The graph on the left

Both end points are represented by closed circles, it means both points are included.

The graph is restricted between the end points from left to right and between the end point and the highest point from bottom to top.

Domain, the set of possible x- coordinates:

• x ∈ [- 2, 6]

Range, the set of possible y- coordinates:

• y ∈ [- 3, 7]

The graph on the right

Both end points are represented by arrows directed to left and right, it means both ends are indefinite but lines are parallel to the x-axis.

It makes x-values infinite but y-values restricted between the two lines.

Domain, the set of possible x- coordinates:

• x ∈ (- ∞, + ∞)

Range, the set of possible y- coordinates:

• y ∈ [1, 5]