Question

NO LINKS!! Please help me with the Domain and Range and Functions Part 4bb​

Answer 1

32.a) Domain: (-6, 6)

32.b) Range: (-6, 2]

32.c) Function: Yes

33.a) Domain: (-6, 6]

33.b) Range: (-1, 5]

33.c) Function: Yes

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 32

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

• (-6, 0) and (6, -6)

As the endpoints are open circles, the x-values are excluded from the domain. Therefore, the domain in interval notation is:

• Domain: (-6, 6)

The smallest y-value is y = -6 and the greatest y-value is y = 2.

y = -6 is excluded from the range since it is the y-value of the open circle endpoint, whereas y = 2 is included in the range. Therefore, the range in interval notation is:

• Range: (-6, 2]

The graph is a function as is each input (x-value) is related to exactly one output (y-value).

Question 33

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

• (-6, -1) and (6, 5)

As the graph is a straight line, the x and y values of the endpoints are the x and y values of the domain and range.

As the (-6, -1) endpoint is an open circle, the values are excluded from the domain and range.

As the (6, 5) endpoint is a closed circle, the values are included in the domain and range.

Therefore, the domain and range in interval notation are:

• Domain: (-6, 6]
• Range: (-1, 5]

The graph is a function as is each input (x-value) is related to exactly 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 32

Domain is:

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

Range is:

• y ∈ (-6, 2], the -6 is excluded as open circle, the 2 is included as part of the graph.

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

Question 33

Domain is:

• x ∈ (- 5, 6], one end is open circle and the other is closed circle.

Range is:

• y ∈ (-1, 5], the -6 is excluded as open circle, the 2 is included as part of the graph.

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