Question

tuesday 9 / 8 / 25
write the set of numbers in set builder notation.
number line image
write the set of numbers in interval notation.
number line image: -3, -2, -1, 0, 1, 2, 3, 4, 5 with open circles
wednesday 9 / 9 / 25
write the set of numbers in set builder notation.
4 < x ≤ 57
write the set of numbers in interval notation.
x < 9
thursday 9 / 10 / 25
write the domain and range of the given graph.
domain : _______________
range : _______________
graph image with dots

Explanation:

Tuesday (Set Builder Notation, assuming the number line has an open circle at 2, so \( x > 2 \))

Step1: Identify the inequality

The number line has an open circle at 2, so \( x > 2 \).

Step2: Write in set builder notation

\( \{x \mid x > 2, x \in \mathbb{R}\} \)

Tuesday (Interval Notation, number line: open at 0, open at 4? Wait, the number line shows open at 0 and open at 4? Wait, the right number line: open circle at 0, open at 4? Wait, the points: -3, -2, -1, 0 (open), 1, 2, 3, 4 (open), 5. So the interval is \( (0, 4) \)? Wait, no, the arrows: left of 0? No, the left arrow: from 0 (open) to left? Wait, no, the number line: open at 0, open at 4, so the set is between 0 (exclusive) and 4 (exclusive)? Wait, the number line: the line is from 0 (open) to 4 (open), so interval notation is \( (0, 4) \). Wait, maybe I misread. Let's recheck: the number line has open circle at 0 and open at 4, so the set is \( 0 < x < 4 \), so interval \( (0, 4) \).

Step1: Identify endpoints

Open circle at 0 (exclusive), open at 4 (exclusive).

Step2: Write interval notation

\( (0, 4) \)

Wednesday (Set Builder Notation for \( 4 < x \leq 57 \))

Step1: Translate inequality to set builder

\( \{x \mid 4 < x \leq 57, x \in \mathbb{R}\} \)

Wednesday (Interval Notation for \( x < 9 \))

Answer:

(Range):

Step1: List y-coordinates

From the graph, y-values are -2, -1, 0, 1.

Step2: Write range

\( \{-2, -1, 0, 1\} \)

Tuesday (Set Builder) Answer: \( \boldsymbol{\{x \mid x > 2, x \in \mathbb{R}\}} \) (if open at 2) or adjusted if number line is different. Wait, original number line: maybe open at 2, so \( x > 2 \).

Tuesday (Interval) Answer: \( \boldsymbol{(0, 4)} \) (if open at 0 and 4)

Wednesday (Set Builder) Answer: \( \boldsymbol{\{x \mid 4 < x \leq 57, x \in \mathbb{R}\}} \)

Wednesday (Interval) Answer: \( \boldsymbol{(-\infty, 9)} \)

Thursday (Domain) Answer: \( \boldsymbol{\{-2, 0, 2\}} \)

Thursday (Range) Answer: \( \boldsymbol{\{-2, -1, 0, 1\}} \)