Express the given interval in set builder notation and graph. (−∞, 0]

• A. {$x\left|x\right.$ ≤ 0}
• B. {$x\mid x$ < 0}
• C. {$x\mid x$ > 0}
• D. $\left\lbrace x|x\ge0\right\rbrace$

Answer: (A)

Verified step by step guidance

1. Identify the interval notation given: (−∞, 0]. This means all numbers less than or equal to 0.
2. Understand that in set builder notation, this interval can be expressed as {x | x ≤ 0}. This reads as 'the set of all x such that x is less than or equal to 0'.
3. To graph this interval, note that it includes all numbers to the left of 0, extending infinitely in the negative direction.
4. The graph will have a solid dot at 0, indicating that 0 is included in the interval, and a line extending to the left towards negative infinity.
5. Review the provided graphs: The correct graph will have a solid dot at 0 and a line extending to the left, matching the interval (−∞, 0].