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}. graph. interval notation. choose the correct graph of the interval described by {x | x < - 8}. a. graph with arrow starting from - 8 and going left b. graph with arrow starting from - 8 and going right c. graph with arrow starting from - 8 and going left with a closed - end at - 8 d. graph with arrow starting from - 8 and going right with a closed - end at - 8

Explanation:

Step1: Analyze set - notation meaning

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

Step2: Determine graph characteristics

On a number - line graph, for $x < - 8$, we use an open circle at $x=-8$ (because $x$ is strictly less than - 8, not equal to it) and draw an arrow to the left to represent all the values less than - 8.

Step3: Determine interval notation

The interval notation for all real numbers $x$ such that $x < - 8$ is $(-\infty,-8)$.

The correct graph has an open circle at - 8 and an arrow pointing to the left. Among the given graphs (assuming the standard way of graphing intervals on a number - line), the correct graph is the one with an open circle at - 8 and an arrow pointing left.

Answer:

The set notation is $\{x|x < - 8\}$, the interval notation is $(-\infty,-8)$. The correct graph is the one with an open - circle at $x = - 8$ and an arrow pointing to the left.