This math topic focuses on translating set builder notations to inequality expressions for domain and range, particularly involving unions of intervals. The problems help enhance understanding of how various intervals represented in set builder form can be visualized and translated into inequalities on a number line. Students assess multiple choice answers to determine the correct inequality that corresponds to graphical representations. This involves critical thinking around endpoint inclusion and the accurate use of inequality symbols (<, ≤, >, ≥) to define the intervals correctly.

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

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Function Domain/Range Definition - Set Builder to Inequality (With Union)
1
What inequality describes domain on this number line?
A LaTex expression showing \{X \in \mathbb{{R}} \vert X \le 6\text{{ or }}8 < X < 11\}
a A LaTex expression showing X < 6\text{{ or }}8 \le X
b A LaTex expression showing X \le 6\text{{ or }}8 < X < 11
2
What inequality describes range on this number line?
A LaTex expression showing \{Y \in \mathbb{{R}} \vert Y < 1\text{{ or }}3 < Y < 12\}
a A LaTex expression showing Y < 1\text{{ or }}3 \le Y < 12
b A LaTex expression showing Y < 1\text{{ or }}3 < Y < 12
3
What inequality describes range on this number line?
A LaTex expression showing \{Y \in \mathbb{{R}} \vert Y < 6\text{{ or }}8 < Y\}
a A LaTex expression showing Y < 6\text{{ or }}8 < Y
b A LaTex expression showing Y < 6\text{{ or }}8 \le Y
4
What inequality describes domain on this number line?
A LaTex expression showing \{X \in \mathbb{{R}} \vert 0 < X < 6\text{{ or }}10 \le X < 14\}
a A LaTex expression showing X < 6\text{{ or }}10 \le X < 14
b A LaTex expression showing 0 < X < 6\text{{ or }}10 \le X < 14
5
What inequality describes range on this number line?
A LaTex expression showing \{Y \in \mathbb{{R}} \vert Y < 5\text{{ or }}6 < Y\}
a A LaTex expression showing Y < 5\text{{ or }}6 < Y
b A LaTex expression showing Y \le 5\text{{ or }}6 < Y \le 11
6
What inequality describes range on this number line?
A LaTex expression showing \{Y \in \mathbb{{R}} \vert -1 \le Y < 5\text{{ or }}5 < Y\}
a A LaTex expression showing -1 \le Y < 5\text{{ or }}5 < Y
b A LaTex expression showing Y \le 5\text{{ or }}5 \le Y
7
What inequality describes domain on this number line?
A LaTex expression showing \{X \in \mathbb{{R}} \vert X \le -3\text{{ or }}-2 \le X\}
a A LaTex expression showing X \le -3\text{{ or }}-2 \le X \le 5
b A LaTex expression showing X \le -3\text{{ or }}-2 \le X
8
What inequality describes range on this number line?
A LaTex expression showing \{Y \in \mathbb{{R}} \vert Y \le 6\text{{ or }}7 < Y\}
a A LaTex expression showing Y \le 6\text{{ or }}7 < Y
b A LaTex expression showing -8 < Y \le 6\text{{ or }}7 \le Y