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Function Domain - Fraction Linear over Quadratic (Real Roots) to Domain Definition

Level 1

This math topic focuses on determining the domain of functions where the numerator is linear and the denominator is quadratic with real roots. Specifically, students are tasked with identifying the sets that describe the domain of these functions. The functions are presented as algebraic fractions, and students need to consider values that satisfy the function’s condition without causing undefined expressions (like division by zero). As part of a broader unit encompassing Functions - Domain and Range Solving Practice, it sharpens skills in analyzing function structure, solving inequalities, and defining valid input values for real-world applications.

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

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Function Domain - Fraction Linear over Quadratic (Real Roots) to Domain Definition Worksheet

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Function Domain - Fraction Linear over Quadratic (Real Roots) to Domain Definition
1
What set describes the domain of this function?
A LaTex expression showing f(x) = -1x+2 over 3x to the power of 2 -9x-12
a A LaTex expression showing \{X \in \mathbb{{R}} \vert -5 \le X < -1\text{{ or }}-1 < X < 4\text{{ or }}-4 < X < 4\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -1\text{{ or }}-1 < X < 4\text{{ or }}4 < X\}
2
What set describes the domain of this function?
A LaTex expression showing f(x) = 1x-5 over 5x to the power of 2 -5x-0
a A LaTex expression showing \{X \in \mathbb{{R}} \vert -1 < X < 1\text{{ or }}0 \le X \le 1\text{{ or }}-1 < X < 1\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X < 0\text{{ or }}0 < X < 1\text{{ or }}1 < X\}
3
What set describes the domain of this function?
A LaTex expression showing f(x) = 1x-4 over -1x to the power of 2 -2x+8
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -4\text{{ or }}-4 \le X \le 2\text{{ or }}2 < X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -4\text{{ or }}-4 < X < 2\text{{ or }}2 < X\}
4
What set describes the domain of this function?
A LaTex expression showing f(x) = -1x-1 over 2x to the power of 2 +4x-16
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -4\text{{ or }}-4 < X < 2\text{{ or }}2 < X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -4\text{{ or }}-4 < X < 2\text{{ or }}-2 < X < 2\}
5
What set describes the domain of this function?
A LaTex expression showing f(x) = -1x-1 over 1x to the power of 2 -8x-20
a A LaTex expression showing \{X \in \mathbb{{R}} \vert -2 < X < 2\text{{ or }}-2 \le X \le 10\text{{ or }}10 \le X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -2\text{{ or }}-2 < X < 10\text{{ or }}10 < X\}
6
What set describes the domain of this function?
A LaTex expression showing f(x) = -1x-4 over 3x to the power of 2 -9x+6
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X < 1\text{{ or }}1 < X < 2\text{{ or }}2 < X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X < 1\text{{ or }}1 < X < 2\text{{ or }}-2 < X < 2\}
7
What set describes the domain of this function?
A LaTex expression showing f(x) = 1x-2 over -1x to the power of 2 -8x-0
a A LaTex expression showing \{X \in \mathbb{{R}} \vert -8 \le X < -5\text{{ or }}-8 \le X \le 0\text{{ or }}-1 < X < 1\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -8\text{{ or }}-8 < X < 0\text{{ or }}0 < X\}
8
What set describes the domain of this function?
A LaTex expression showing f(x) = -1x+3 over 1x to the power of 2 -9x+20
a A LaTex expression showing \{X \in \mathbb{{R}} \vert -1 < X < 4\text{{ or }}4 \le X \le 5\text{{ or }}5 \le X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X < 4\text{{ or }}4 < X < 5\text{{ or }}5 < X\}