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

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

Answer: (A)

Verified step by step guidance

1. Identify the given interval: The interval is (−∞, 0], which means it includes all numbers less than or equal to 0.
2. Understand the notation: The round parenthesis '(' indicates that −∞ is not included in the interval, while the square bracket ']' indicates that 0 is included.
3. Express in set builder notation: The interval (−∞, 0] can be expressed as {x | x ≤ 0}, which reads as 'the set of all x such that x is less than or equal to 0.'
4. Graph the interval: On a number line, draw a line extending to the left from 0, with a closed dot at 0 to indicate that 0 is included in the interval.
5. Review the graph: Ensure that the line extends indefinitely to the left, representing all numbers less than 0, and that the closed dot at 0 correctly shows inclusion of 0 in the interval.