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 | x < -8} choose the correct graph of the interval described by {x | x < -8} a. graph with arrow pointing left ending at -8 with an open - circle b. graph with arrow pointing left ending at -8 with a closed - circle c. graph with arrow pointing left ending at -8 with an open - circle d. graph with arrow pointing left ending at -8 with a closed - circle write interval notation describing the interval {x | x < -8}. set notation: {x | x < -8} interval notation: (type your answer in interval notation.)

Explanation:

Step1: Understand set - notation meaning

The set - notation $\{x|x < - 8\}$ represents all real numbers $x$ that are less than $-8$.

Step2: Determine the graph

On a number line, for $x < - 8$, we use an open - circle at $-8$ (because $-8$ is not included in the set) and an arrow pointing to the left. Option B has an open - circle at $-8$ and an arrow pointing to the left, so it is the correct graph.

Step3: Write interval notation

In interval notation, when the set includes all numbers less than a value $a$ (but not $a$ itself), we write $(-\infty,a)$. Here $a=-8$, so the interval notation is $(-\infty,-8)$.

Answer:

B. The graph with an open - circle at $-8$ and an arrow pointing to the left
$(-\infty,-8)$