Function Domain/Range Definition - Inequality to Set Builder (With Union) (Level 1) - Mobius Math Academy

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

Level 1

This math topic focuses on defining the domain and range of functions using inequality notation and translating it into a formal set-builder notation, often involving unions of intervals. It practices the ability to interpret and write the correct mathematical expressions for the range and domain of given inequalities, enhancing understanding of interval notations and the set-builder form within the context of mathematical functions.

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 Set Builder (With Union) Worksheet

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

What set describes the range of this inequality?

$A LaTex expression showing -1 \le Y < 2\text{{ or }}2 < Y \le 7$

a $A LaTex expression showing \{Y \in \mathbb{{R}} \vert Y < 2\text{{ or }}2 \le Y < 7\}$

b $A LaTex expression showing \{Y \in \mathbb{{R}} \vert -1 \le Y < 2\text{{ or }}2 < Y \le 7\}$

What set describes the range of this inequality?

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

a $A LaTex expression showing \{Y \in \mathbb{{R}} \vert Y < 2\text{{ or }}4 \le Y\}$

b $A LaTex expression showing \{Y \in \mathbb{{R}} \vert Y \le 2\text{{ or }}4 \le Y \le 13\}$

What set describes the range of this inequality?

$A LaTex expression showing 1 \le Y < 9\text{{ or }}9 < Y \le 15$

a $A LaTex expression showing \{Y \in \mathbb{{R}} \vert 1 \le Y < 9\text{{ or }}9 < Y \le 15\}$

b $A LaTex expression showing \{Y \in \mathbb{{R}} \vert 1 \le Y < 9\text{{ or }}9 \le Y < 15\}$

What set describes the range of this inequality?

$A LaTex expression showing Y < 5\text{{ or }}5 < Y \le 13$

a $A LaTex expression showing \{Y \in \mathbb{{R}} \vert 0 \le Y < 5\text{{ or }}5 \le Y \le 13\}$

b $A LaTex expression showing \{Y \in \mathbb{{R}} \vert Y < 5\text{{ or }}5 < Y \le 13\}$

What set describes the domain of this inequality?

$A LaTex expression showing 1 < X \le 4\text{{ or }}7 \le X$

a $A LaTex expression showing \{X \in \mathbb{{R}} \vert 1 < X \le 4\text{{ or }}7 \le X\}$

b $A LaTex expression showing \{X \in \mathbb{{R}} \vert 1 \le X < 4\text{{ or }}7 \le X\}$

What set describes the domain of this inequality?

$A LaTex expression showing 2 < X \le 6\text{{ or }}9 < X \le 16$

a $A LaTex expression showing \{X \in \mathbb{{R}} \vert 2 < X \le 6\text{{ or }}9 < X \le 16\}$

b $A LaTex expression showing \{X \in \mathbb{{R}} \vert 2 < X \le 6\text{{ or }}9 \le X \le 16\}$

What set describes the domain of this inequality?

$A LaTex expression showing X \le -7\text{{ or }}-4 \le X$

a $A LaTex expression showing \{X \in \mathbb{{R}} \vert X \le -7\text{{ or }}-4 \le X\}$

b $A LaTex expression showing \{X \in \mathbb{{R}} \vert -10 < X \le -7\text{{ or }}-4 \le X\}$

What set describes the range of this inequality?

$A LaTex expression showing 4 < Y < 7\text{{ or }}8 \le Y < 14$

a $A LaTex expression showing \{Y \in \mathbb{{R}} \vert 4 \le Y < 7\text{{ or }}8 \le Y < 14\}$

b $A LaTex expression showing \{Y \in \mathbb{{R}} \vert 4 < Y < 7\text{{ or }}8 \le Y < 14\}$