Question

there are three ways of describing an interval. for the interval described using set notation, graph the interval and write interval notation. set notation \\(\\{x \mid x < -1\\}\\) choose the correct graph of the interval described by \\(\\{x \mid x < -1\\}\\). write interval notation describing the interval \\(\\{x \mid x < -1\\}\\). set notation \\(\\{x \mid x < -1\\}\\) (type your answer in interval notation)

Explanation:

Part 1: Choose the correct graph

The set notation \(\{x | x < -1\}\) represents all real numbers less than \(-1\). On a number line, this is shown by an open circle (since \(-1\) is not included) and an arrow pointing to the left (towards negative infinity). Looking at the options, option B has an open circle at \(-1\) and the arrow pointing left, which matches the set notation.

Step 1: Recall interval notation rules

For all numbers less than a value \(a\) (not including \(a\)), the interval notation is \((-\infty, a)\). Here, \(a = -1\) and \(x\) is less than \(-1\) (not including \(-1\)).

Step 2: Apply the rule

Using the rule, the interval notation for \(x < -1\) is \((-\infty, -1)\).

Answer:

B. The graph with an open circle at -1 and an arrow pointing to the left (towards more negative numbers)

Part 2: Write interval notation for \(\{x | x < -1\}\)