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Function Domain - Fraction Integer over Linear to Domain Definition

Level 1

This math topic focuses on determining the domain of rational functions, where the denominator includes a linear expression. The students are provided with functions of the form \( f(x) = \frac{a}{bx+c} \), and they must identify the valid values of \( x \) that do not make the denominator zero, thereby avoiding undefined expressions. Each question presents a function with different coefficients in the linear denominator, and multiple-choice answers detail various potential domains using set notation and inequality symbols, testing the student's understanding of restrictions in rational functions.

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

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Function Domain - Fraction Integer over Linear to Domain Definition Worksheet

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Math worksheet on 'Function Domain - Fraction Integer over Linear to Domain Definition (Level 1)'. Part of a broader unit on 'Functions - Domain and Range Solving - Practice' Learn online: app.mobius.academy/math/units/functions_domain_range_solving_practice/
1
What set describes the domain of this function?
A LaTex expression showing f(x) = -3 over -1x-5
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -5\text{{ or }}-5 < X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X \le -5\text{{ or }}-5 \le X\}
2
What set describes the domain of this function?
A LaTex expression showing f(x) = -2 over -1x+4
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X < 4\text{{ or }}4 < X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert -4 < X < 4\text{{ or }}-4 < X < 4\}
3
What set describes the domain of this function?
A LaTex expression showing f(x) = 4 over 1x+1
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -1\text{{ or }}-1 < X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert -1 < X < 1\text{{ or }}-1 < X\}
4
What set describes the domain of this function?
A LaTex expression showing f(x) = 3 over -1x-0
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X < 0\text{{ or }}0 < X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert -1 < X < 1\text{{ or }}0 \le X\}
5
What set describes the domain of this function?
A LaTex expression showing f(x) = 4 over 1x+3
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -3\text{{ or }}-3 < X < 3\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -3\text{{ or }}-3 < X\}
6
What set describes the domain of this function?
A LaTex expression showing f(x) = -5 over -1x-2
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X \le -2\text{{ or }}-2 < X < 2\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -2\text{{ or }}-2 < X\}
7
What set describes the domain of this function?
A LaTex expression showing f(x) = 5 over 1x+3
a A LaTex expression showing \{X \in \mathbb{{R}} \vert -3 < X < 3\text{{ or }}-3 < X < 3\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -3\text{{ or }}-3 < X\}