Question

NO LINKS!! Please help me with these graphs Part 2a​

Answer 1

1. Domain: (-∞, ∞) Range: (-∞, 4]

2. Domain: (-∞, ∞) Range: [3, ∞)

3. Domain: [-2, ∞) Range: [-3, ∞)

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

As there are arrows at both endpoints of the curve, the domain of the function is unrestricted.

• Domain: (-∞, ∞)

The curve has a maximum point at (2, 4) and continues indefinitely towards negative infinity at both endpoints.

Therefore, the range of the function is restricted.

• Range: (-∞, 4]

Question 2

As there are arrows at both endpoints of the function, the domain is unrestricted.

• Domain: (-∞, ∞)

The function has a minimum point at y = 3.

When x > -2, the line continues indefinitely at y = 3.

When x < -2, the line continues indefinitely towards infinity.

Therefore, the range of the function is restricted.

• Range: [3, ∞)

Question 3

The domain of the function is restricted since there is a closed circle at one endpoint: (-2, -3). When x > -2, the line continues indefinitely towards infinity.

• Domain: [-2, ∞)

The function has a minimum point at (-2, -3). As x continues towards infinity, so does y.

Therefore, the range of the function is restricted.

• Range: [-3, ∞)

Answer 2

Left graph.

Domain: all real numbers.

Range: y ≤ 4

Middle graph.

Domain: all real numbers

Range: y ≥ 3

Right graph.

Domain: x ≥ -2

Range: y ≥ -3