This topic focuses on converting set builder notation of functions' domains and ranges into interval notation, with special attention to unions of intervals. It explores various conditions under which specific real number values fall within defined set parameters, such as inequalities with closed or open boundaries, and how these are represented using interval notation. The problems require understanding mathematical expressions of domain and range, and how they translate to graphical interval representations, including unions where necessary.

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

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Function Domain/Range Definition - Set Builder to Interval (With Union)
1
What interval describes this range?
A LaTex expression showing \{Y \in \mathbb{{R}} \vert Y < -1\text{{ or }}2 \le Y\}
a A LaTex expression showing ( -\infty, -1)\cup[2, \infty)
b A LaTex expression showing (-7, -1]\cup(2, \infty)
2
What interval describes this range?
A LaTex expression showing \{Y \in \mathbb{{R}} \vert 2 < Y \le 5\text{{ or }}9 \le Y\}
a A LaTex expression showing [2, 5]\cup[9, \infty)
b A LaTex expression showing (2, 5]\cup[9, \infty)
3
What interval describes this domain?
A LaTex expression showing \{X \in \mathbb{{R}} \vert -8 < X < 7\text{{ or }}7 < X \le 15\}
a A LaTex expression showing (-8, 7]\cup(7, 15)
b A LaTex expression showing (-8, 7)\cup(7, 15]
4
What interval describes this range?
A LaTex expression showing \{Y \in \mathbb{{R}} \vert -1 \le Y \le 8\text{{ or }}12 < Y \le 18\}
a A LaTex expression showing [-1, 8]\cup(12, 18]
b A LaTex expression showing [-1, 8]\cup(12, \infty)
5
What interval describes this domain?
A LaTex expression showing \{X \in \mathbb{{R}} \vert -10 \le X \le 1\text{{ or }}5 < X < 14\}
a A LaTex expression showing ( -\infty, 1]\cup(5, 14)
b A LaTex expression showing [-10, 1]\cup(5, 14)
6
What interval describes this range?
A LaTex expression showing \{Y \in \mathbb{{R}} \vert -6 < Y < 1\text{{ or }}4 < Y\}
a A LaTex expression showing (-6, 1)\cup(4, \infty)
b A LaTex expression showing [-6, 1]\cup[4, 13]
7
What interval describes this range?
A LaTex expression showing \{Y \in \mathbb{{R}} \vert -6 < Y < 4\text{{ or }}5 < Y \le 9\}
a A LaTex expression showing ( -\infty, 4]\cup[5, 9)
b A LaTex expression showing (-6, 4)\cup(5, 9]
8
What interval describes this domain?
A LaTex expression showing \{X \in \mathbb{{R}} \vert 2 \le X < 9\text{{ or }}13 < X \le 21\}
a A LaTex expression showing [2, 9)\cup(13, 21]
b A LaTex expression showing [2, 9)\cup[13, 21]