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

Level 1

This math topic focuses on translating between verbal descriptions of domains and ranges of functions to mathematical inequalities, specifically involving unions which represent composite conditions. The problems challenge learners to convert phrases like "all real numbers less than -2 OR greater than or equal to 2 and less than or equal to 9" into appropriate inequality statements, integrating the use of the union symbol in inequalities.

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

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

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Function Domain/Range Definition - Words to Inequality (With Union)
1
All real numbers greater than 2 and less than or equal to 5 OR greater than or equal to 9 and less than 18
What inequality describes this domain?
a A LaTex expression showing 2 < X \le 5\text{{ or }}9 \le X < 18
b A LaTex expression showing 2 < X \le 5\text{{ or }}9 \le X
2
All real numbers greater than 2 and less than or equal to 8 OR greater than 11
What inequality describes this range?
a A LaTex expression showing 2 < Y \le 8\text{{ or }}11 < Y
b A LaTex expression showing 2 < Y \le 8\text{{ or }}11 \le Y
3
All real numbers greater than -2 and less than 7 OR greater than 11 and less than 17
What inequality describes this domain?
a A LaTex expression showing -2 < X < 7\text{{ or }}11 < X < 17
b A LaTex expression showing -2 < X < 7\text{{ or }}11 \le X < 17
4
All real numbers less than -2 OR greater than or equal to 2 and less than or equal to 9
What inequality describes this range?
a A LaTex expression showing Y < -2\text{{ or }}2 \le Y \le 9
b A LaTex expression showing Y < -2\text{{ or }}2 \le Y < 9
5
All real numbers greater than or equal to -4 and less than or equal to 5 OR greater than 9 and less than 12
What inequality describes this range?
a A LaTex expression showing -4 \le Y \le 5\text{{ or }}9 < Y < 12
b A LaTex expression showing -4 < Y \le 5\text{{ or }}9 \le Y < 12
6
All real numbers less than 4 OR greater than or equal to 6 and less than or equal to 10
What inequality describes this range?
a A LaTex expression showing Y < 4\text{{ or }}6 \le Y \le 10
b A LaTex expression showing -6 \le Y \le 4\text{{ or }}6 < Y < 10
7
What inequality describes this range?
All real numbers less than or equal to -1 OR greater than 0
a A LaTex expression showing Y < -1\text{{ or }}0 < Y
b A LaTex expression showing Y \le -1\text{{ or }}0 < Y
8
All real numbers less than 4 OR greater than 4 and less than or equal to 7
What inequality describes this domain?
a A LaTex expression showing -4 \le X \le 4\text{{ or }}4 < X < 7
b A LaTex expression showing X < 4\text{{ or }}4 < X \le 7