Question

which of the following graphs corresponds to the following set? $(-infty, -4)$ question help: message instructor

Explanation:

Step1: Analyze the interval \((-\infty, -4)\)

The interval \((-\infty, -4)\) means all real numbers less than \(-4\). In interval notation, the parenthesis around \(-4\) indicates that \(-4\) is not included in the set.

Step2: Analyze the number line graphs

• For a number line representing \(x < -4\) (where \(-4\) is not included), we use an open circle at \(-4\) (since \(-4\) is not in the set) and an arrow pointing to the left (towards negative infinity, indicating all numbers less than \(-4\)).

• Let's check each graph:
• First graph: Open circle at \(-4\), arrow to the left (towards \(-\infty\)) – this matches \(x < -4\) (i.e., \((-\infty, -4)\)).
• Second graph: Closed circle at \(-4\), arrow to the right – this represents \(x \geq -4\), which is not our set.
• Third graph: Closed circle at \(-4\), arrow to the left – this represents \(x \leq -4\), which is not our set (we need \(x < -4\), not including \(-4\)).
• Fourth graph: Open circle at \(-4\), arrow to the right – this represents \(x > -4\), which is not our set.

Answer:

The first graph (with open circle at -4 and arrow to the left)