This math topic focuses on translating descriptions of intervals involving real numbers or integers into set builder notation, incorporating union conditions. The problems ask the student to match verbose expressions with their correct set builder notations, involving scenarios like "greater than and less than" conditions, and using both open and closed intervals. The exercises enhance understanding of domain and range definitions in mathematical functions, specifically developing the student's ability to work with and convert between different forms of representing numerical sets.

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Function Domain/Range Definition - Words to Set Builder (With Union) Worksheet

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Function Domain/Range Definition - Words to Set Builder (With Union)
1
All real numbers greater than -1 and less than or equal to 4 OR greater than or equal to 6
What set describes this range?
a A LaTex expression showing \{Y \in \mathbb{{R}} \vert -1 < Y \le 4\text{{ or }}6 \le Y\}
b A LaTex expression showing \{Y \in \mathbb{{R}} \vert -1 < Y < 4\text{{ or }}6 < Y\}
2
All integers greater than -5 and less than 5 OR greater than or equal to 6 and less than or equal to 12
What set describes this domain?
a A LaTex expression showing \{X \in \mathbb{{Z}} \vert X < 5\text{{ or }}6 < X \le 12\}
b A LaTex expression showing \{X \in \mathbb{{Z}} \vert -5 < X < 5\text{{ or }}6 \le X \le 12\}
3
All real numbers greater than 0 and less than or equal to 5 OR greater than or equal to 8 and less than 11
What set describes this range?
a A LaTex expression showing \{Y \in \mathbb{{R}} \vert 0 < Y \le 5\text{{ or }}8 < Y < 11\}
b A LaTex expression showing \{Y \in \mathbb{{R}} \vert 0 < Y \le 5\text{{ or }}8 \le Y < 11\}
4
All integers greater than or equal to 1 and less than or equal to 7 OR greater than or equal to 11
What set describes this range?
a A LaTex expression showing \{Y \in \mathbb{{Z}} \vert 1 \le Y \le 7\text{{ or }}11 \le Y\}
b A LaTex expression showing \{Y \in \mathbb{{Z}} \vert 1 \le Y < 7\text{{ or }}11 \le Y \le 16\}
5
What set describes this domain?
All integers less than 6 OR greater than 10
a A LaTex expression showing \{X \in \mathbb{{Z}} \vert X < 6\text{{ or }}10 \le X\}
b A LaTex expression showing \{X \in \mathbb{{Z}} \vert X < 6\text{{ or }}10 < X\}
6
What set describes this domain?
All real numbers less than or equal to 7 OR greater than 10
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X \le 7\text{{ or }}10 \le X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X \le 7\text{{ or }}10 < X\}
7
All real numbers less than 9 OR greater than or equal to 11 and less than 14
What set describes this range?
a A LaTex expression showing \{Y \in \mathbb{{R}} \vert Y < 9\text{{ or }}11 \le Y < 14\}
b A LaTex expression showing \{Y \in \mathbb{{R}} \vert Y \le 9\text{{ or }}11 \le Y \le 14\}
8
All integers greater than or equal to -5 and less than or equal to 7 OR greater than 11
What set describes this domain?
a A LaTex expression showing \{X \in \mathbb{{Z}} \vert -5 \le X \le 7\text{{ or }}11 < X\}
b A LaTex expression showing \{X \in \mathbb{{Z}} \vert X \le 7\text{{ or }}11 \le X\}