Question

NO LINKS!! Please help me with the Domain and Range and Functions Part 3bb​

Answer 1

30.a) Domain: [-6, 6]

30.b) Range: [-3, 7]

30.c) Function: No

31.a) Domain: [-2, 2]

31.b) Range: [-6, 6]

31.c) Function: No

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 30

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

The smallest x-value is x = -6 and the greatest x-value is x = 6.

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

Therefore, the domain and range in interval notation are:

• Domain: [-6, 6]
• Range: [-3, 7]

The graph is a not a function as almost all the inputs (x-values) are related to more than one output (y-value).

Question 31

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

• (-6, 0) and (2, 6)

Both endpoints are closed circles, so the values are included in the domain and range.

The smallest x-value is x = -2 and the greatest x-value is x = 2.

Therefore, the domain in interval notation is:

• Domain: [-2, 2]

The smallest y-value is y = -6 and the greatest y-value is y = 6.

Therefore, the range in interval notation is:

• Range: [-6, 6]

The graph is a not a function as not all inputs (x-values) are related to one output (y-value).

Answer 2

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

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

Question 30

Domain is:

• x ∈ [- 6, 6], both ends included as part of graph.

Range is:

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

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

Question 31

Domain is:

• x ∈ [- 2, 2], one end is is part of the graph and the other is closed circle.

Range is:

• y ∈ [-6, 6], both ends included as closed circles.

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