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Function Domain/Range Definition - Inequality to Words (With Union)

Level 1

This topic involves interpreting inequalities describing the domain and range of functions and translating them into verbal descriptions. It specifically focuses on scenarios where sets are combined using union, indicating a range that consists of multiple intervals. For each problem, users are presented with an inequality and multiple choice answers to select the correct verbal interpretation of the inequality. This skill falls under the broader category of understanding functions’ domain and range, crucial in algebra and precalculus contexts.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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

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Function Domain/Range Definition - Inequality to Words (With Union)
1
What range does this inequality describe?
A LaTex expression showing Y \le 9\text{{ or }}11 \le Y \le 16
a
All real numbers greater than or equal to 3 and less than 9 OR greater than 11 and less than or equal to 16
b
All real numbers less than or equal to 9 OR greater than or equal to 11 and less than or equal to 16
2
What range does this inequality describe?
A LaTex expression showing Y \le 5\text{{ or }}6 \le Y < 12
a
All real numbers less than or equal to 5 OR greater than or equal to 6 and less than 12
b
All real numbers less than 5 OR greater than 6 and less than or equal to 12
3
What range does this inequality describe?
A LaTex expression showing -9 < Y \le 4\text{{ or }}7 \le Y
a
All real numbers greater than -9 and less than or equal to 4 OR greater than or equal to 7
b
All real numbers greater than -9 and less than 4 OR greater than or equal to 7
4
What domain does this inequality describe?
A LaTex expression showing X \le 7\text{{ or }}8 \le X < 13
a
All real numbers less than or equal to 7 OR greater than or equal to 8 and less than 13
b
All real numbers less than 7 OR greater than 8 and less than 13
5
What range does this inequality describe?
A LaTex expression showing Y < 2\text{{ or }}2 < Y < 8
a
All real numbers less than 2 OR greater than 2 and less than 8
b
All real numbers greater than -6 and less than or equal to 2 OR greater than 2
6
What range does this inequality describe?
A LaTex expression showing Y \le 1\text{{ or }}3 \le Y
a
All real numbers less than or equal to 1 OR greater than or equal to 3
b
All real numbers less than 1 OR greater than 3
7
What domain does this inequality describe?
A LaTex expression showing -2 \le X < 1\text{{ or }}2 \le X
a
All real numbers greater than or equal to -2 and less than 1 OR greater than or equal to 2
b
All real numbers greater than -2 and less than 1 OR greater than 2
8
What range does this inequality describe?
A LaTex expression showing Y < 0\text{{ or }}2 < Y \le 10
a
All real numbers less than or equal to 0 OR greater than or equal to 2 and less than or equal to 10
b
All real numbers less than 0 OR greater than 2 and less than or equal to 10