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

Level 1

This math topic focuses on converting inequalities into interval notation, specifically incorporating unions to describe domains and ranges of functions. The problems involve interpreting inequalities, such as "X < 9 or 12 < X," and selecting from provided interval notation options like "(-∞, 9) ∪ (12, ∞)." This practice helps develop skills in understanding and applying mathematical expressions for function boundaries within a range of real numbers, critical for topics in calculus and advanced algebra.

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

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

What interval describes this range?

$A LaTex expression showing -6 < Y < 2\text{{ or }}4 \le Y$

a $A LaTex expression showing (-6, 2)\cup[4, \infty)$

b $A LaTex expression showing [-6, 2]\cup(4, \infty)$

What interval describes this range?

$A LaTex expression showing 2 < Y \le 5\text{{ or }}9 < Y < 14$

a $A LaTex expression showing (2, 5]\cup(9, 14)$

b $A LaTex expression showing [2, 5]\cup[9, 14)$

$A LaTex expression showing Y < 5\text{{ or }}8 \le Y$

What interval describes this range?

a $A LaTex expression showing ( -\infty, 5)\cup(8, \infty)$

b $A LaTex expression showing ( -\infty, 5)\cup[8, \infty)$

What interval describes this domain?

$A LaTex expression showing -6 \le X < 5\text{{ or }}7 \le X$

a $A LaTex expression showing [-6, 5)\cup[7, \infty)$

b $A LaTex expression showing (-6, 5)\cup[7, \infty)$

What interval describes this range?

$A LaTex expression showing -6 < Y \le -3\text{{ or }}-2 < Y$

a $A LaTex expression showing [-6, -3)\cup[-2, \infty)$

b $A LaTex expression showing (-6, -3]\cup(-2, \infty)$

What interval describes this range?

$A LaTex expression showing 0 \le Y \le 7\text{{ or }}10 < Y \le 15$

a $A LaTex expression showing [0, 7]\cup(10, 15]$

b $A LaTex expression showing (0, 7)\cup(10, 15]$

What interval describes this domain?

$A LaTex expression showing -5 < X < -1\text{{ or }}3 < X < 8$

a $A LaTex expression showing (-5, -1]\cup(3, 8]$

b $A LaTex expression showing (-5, -1)\cup(3, 8)$

What interval describes this domain?

$A LaTex expression showing 3 \le X < 7\text{{ or }}7 < X < 10$

a $A LaTex expression showing [3, 7)\cup(7, 10)$

b $A LaTex expression showing ( -\infty, 7]\cup(7, 10]$