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 < -6\\}
graph
interval notation
...
choose the correct graph of the interval described by \\{x \mid x < -6\\}.
\\(\bigcirc\\) a
\\(\bigcirc\\) b
\\(\bigcirc\\) c
\\(\bigcirc\\) d
write interval notation describing the interval \\{x \mid x < -6\\}.
set notation \\{x \mid x < -6\\}
interval notation
(type your answer in interval notation)

Explanation:

Step1: Identify graph for $x < -6$

The inequality $x < -6$ means all values less than -6, so the graph has an open circle at -6 and an arrow pointing left. This matches Option A.

Step2: Convert set notation to interval notation

For all real numbers less than -6, we use $(-\infty, -6)$ where $-\infty$ represents the lower bound and the parenthesis shows -6 is not included.

Answer:

Correct graph: A. (Graph with open circle at -6, arrow left)
Interval notation: $(-\infty, -6)$