This math topic focuses on determining the domain of a function where the function format is a fraction with an integer numerator over a quadratic expression with real roots. Specifically, the problems require analyzing and identifying sets that describe possible values of x such that the function outputs a real number. This involves ensuring the denominator does not equal zero, implying the necessity of understanding and working with quadratic inequalities. The skill practiced is crucial in higher mathematics, particularly in calculus and algebra where understanding function behavior is essential.

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

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Function Domain - Fraction Integer over Quadratic (Real Roots) to Domain Definition
1
What set describes the domain of this function?
A LaTex expression showing f(x) = -1 over -2x to the power of 2 +2x+24
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -3\text{{ or }}-3 < X < 4\text{{ or }}4 < X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert -3 < X < 3\text{{ or }}-3 \le X \le 4\text{{ or }}-4 < X < 4\}
2
What set describes the domain of this function?
A LaTex expression showing f(x) = -5 over 5x to the power of 2 -10x-15
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -1\text{{ or }}-1 < X < 3\text{{ or }}3 < X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert -1 < X < 3\text{{ or }}-1 < X \le 3\text{{ or }}-3 < X < 3\}
3
What set describes the domain of this function?
A LaTex expression showing f(x) = 1 over 1x to the power of 2 +1x-6
a A LaTex expression showing \{X \in \mathbb{{R}} \vert -3 < X < 3\text{{ or }}-3 \le X \le 2\text{{ or }}2 < X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -3\text{{ or }}-3 < X < 2\text{{ or }}2 < X\}
4
What set describes the domain of this function?
A LaTex expression showing f(x) = 4 over 1x to the power of 2 -7x+10
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X < 2\text{{ or }}2 < X < 5\text{{ or }}5 < X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X \le 2\text{{ or }}2 < X \le 5\text{{ or }}-5 < X < 5\}
5
What set describes the domain of this function?
A LaTex expression showing f(x) = -4 over 2x to the power of 2 -10x-0
a A LaTex expression showing \{X \in \mathbb{{R}} \vert -1 < X < 1\text{{ or }}0 \le X \le 5\text{{ or }}5 < X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X < 0\text{{ or }}0 < X < 5\text{{ or }}5 < X\}
6
What set describes the domain of this function?
A LaTex expression showing f(x) = -5 over 3x to the power of 2 +9x+6
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -2\text{{ or }}-2 < X < -1\text{{ or }}-1 < X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X \le -2\text{{ or }}-2 \le X \le -1\text{{ or }}-1 < X < 1\}
7
What set describes the domain of this function?
A LaTex expression showing f(x) = 2 over 1x to the power of 2 -4x+3
a A LaTex expression showing \{X \in \mathbb{{R}} \vert -1 < X < 1\text{{ or }}1 \le X \le 3\text{{ or }}-3 \le X \le 3\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X < 1\text{{ or }}1 < X < 3\text{{ or }}3 < X\}
8
What set describes the domain of this function?
A LaTex expression showing f(x) = 2 over -2x to the power of 2 -2x+12
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -3\text{{ or }}-3 < X < 2\text{{ or }}2 < X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X \le -3\text{{ or }}-3 \le X \le 2\text{{ or }}-2 < X < 2\}