Question

NO LINKS!! Please help me with the Domain and Range and Functions Part 2bb​

Answer 1

25) Domain: (-6, 6)

Range: [-5, 3)

26) Domain: [-3, 7]

Range: [-1, 5]

Explanation:

Definitions

• An open circle indicates the value is not included in the interval.
• A closed circle indicates the value is included in the interval.
• An arrow shows that the function continues indefinitely in that direction.

Interval notation

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

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

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

Question 25

From inspection of the graph, the endpoints of the continuous curve are:

• (-6, -3) and (6, 3)

As the endpoints are open circles, the values are excluded from the domain and range.

Therefore, the domain in interval notation is:

• Domain: (-6, 6)

The smallest y-value is y = -5 and the greatest y-value is y = 3.

Therefore, the range in interval notation is:

• Range: [-5, 3)

Question 26

The graph is a conic section (ellipse) and therefore it is not a function.

The smallest x-value is x = -3 and the greatest x-value is x = 7.

The smallest y-value is y = -1 and the greatest y-value is y = 5.

Therefore, the domain and range in interval notation are:

• Domain: [-3, 7]
• Range: [-1, 5]

Answer 2

Domain - the set of possible x-coordinates of a function.

Range - the set of possible y-coordinates of a function.

Question 25

Domain is:

• x ∈ (- 6, 6), both ends excluded as open circles.

Range is:

• y ∈ [-5, 3), the lowest point is included as part of graph, the highest value is excluded as open circle..

This is a function as it passes the vertical line test.

Question 26

Domain is:

• x ∈ [- 3, 7], both ends included as part of the graph.

Range is:

• y ∈ [-1, 5], both ends included as part of the graph.

This is not a function as it fails the vertical line test.