Express each set in interval notation: (a) WebAssign Number Line (b) WebAssign Number Line
The Correct Answer and Explanation is:
(a)
The correct interval no
tation is:
[0, 4)
(b)
The correct interval notation is:
(-4, 0]
Explanation
Interval notation is a method used to represent a range of numbers on the number line. It uses parentheses and square brackets to indicate whether the endpoints of the range are included in the set.
- A square bracket [ or ] indicates that the endpoint is included in the interval. On a number line, this is represented by a solid or closed circle (●).
- A parenthesis ( or ) indicates that the endpoint is excluded from the interval. On a number line, this is represented by a hollow or open circle (○).
The notation is always written with the smaller number on the left and the larger number on the right, separated by a comma.
Analysis of Part (a)
- Identify the Endpoints: The shaded region on the number line extends from 0 to 4.
- Examine the Left Endpoint: At the number 0, there is a solid, closed circle (●). This signifies that 0 is included in the set. Therefore, we use a square bracket [ for the left side of the interval.
- Examine the Right Endpoint: At the number 4, there is a hollow, open circle (○). This signifies that 4 is excluded from the set. The set includes all numbers approaching 4, but not 4 itself. Thus, we use a parenthesis ) for the right side of the interval.
Combining these, the interval notation for the set is [0, 4). This represents all real numbers x such that 0 ≤ x < 4.
Analysis of Part (b)
- Identify the Endpoints: The shaded region on this number line spans from -4 to 0.
- Examine the Left Endpoint: At the number -4, there is a hollow, open circle (○). This indicates that -4 is not part of the set. Accordingly, we start the interval notation with a parenthesis (.
- Examine the Right Endpoint: At the number 0, there is a solid, closed circle (●). This means that 0 is included in the set. We close the interval notation with a square bracket ].
Combining these, the interval notation for this set is (-4, 0]. This represents all real numbers x such that -4 < x ≤ 0.thumb_upthumb_down
