Question

NO LINKS!! Please help me with the Domain and Range part 4ii​

Answer 1

9) D: (-4, 4]; R: [-6, -4]

10) D: [-5, -5]; R: (-7, ∞)

Explanation:

You want the domain and range of the relations shown on the given graphs.

Domain

The domain of a relation is the set of x-values for which it is defined. An open circle indicates that point is not included in either the domain or range.

Range

The range of a relation is the set of y-values that the relation produces. An open circle indicates the y-value at that point is not in the range.

9)

The graph has an open circle at x = -4 on the left, and a solid dot at x = 4 on the right. All of the x-values between these have corresponding y-values.

The domain is (-4, 4].

The bottom (minimum) of the curve lies on the line y = -6, so that is the lowest value in the range. The relation produces all y-values between -6 and -4. The solid dot at (4, -4) means -4 is included in the range.

The range is [-6, -4].

10)

The vertical line at x=-5 means -5 is the only value in the domain.

The domain is [-5, -5].

The vertical line extends upward from an open circle at y = -7. The open circle means -7 is not part of the range.

The range is (-7, ∞).

Answer 2

9) Domain: (-4, 4]

Range: [-6, -4]

10) Domain: [-5]

Range: (-7, ∞)

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.

Domain & Range

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 9

From inspection of the graph, the minimum x-value is x = -4 and the maximum x-value is x = 4.

There is an open circle at endpoint (-4, -4). Therefore, x = -4 is not included in the domain.

There is an closed circle at endpoint (4, -4). Therefore, x = 4 is included in the domain.

Therefore, the domain of the relation is restricted: (-4, 4]

From inspection of the graph, the minimum y-value is y = -6 and the maximum y-value is y = -4.

This maximum value is included in the range since there is a closed circle at (4, -4).

Therefore, the range of the relation is restricted: [-6, -4]

Question 10

From inspection of the graph, the line is a vertical line at x = -5.

Therefore, the domain of the relation is restricted to x = -5: [-5]

From inspection of the graph, the minimum y-value is x = -7.

This minimum value is not included in the range since there is an open circle at (-5, -7).

There is an arrow on the other endpoint of the line, indicating that the line continues indefinitely in that direction.

Therefore, the range of the relation is restricted: (-7, ∞)