This math topic focuses on determining the domain of a function in which the numerator is a square root of a linear expression, and the denominator is a linear expression. Students are required to identify valid input values that ensure the function is defined, typically involving conditions where the expression under the square root must be non-negative, and the denominator is non-zero. Each question presents different linear functions where students choose from multiple possible domains.

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Function Domain - Fraction Root of Linear over Linear to Domain Definition Worksheet

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Function Domain - Fraction Root of Linear over Linear to Domain Definition
1
What set describes the domain of this function?
A LaTex expression showing f(x) = \frac{square root of -1x-4}{-1x+5}
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X \le -4\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert -4 \le X\}
2
What set describes the domain of this function?
A LaTex expression showing f(x) = \frac{square root of -1x+2}{1x+5}
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -5\text{{ or }}-5 < X \le 2\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert -5 < X < 5\text{{ or }}-5 \le X < 2\}
3
What set describes the domain of this function?
A LaTex expression showing f(x) = \frac{square root of -1x+5}{-1x+3}
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X < 3\text{{ or }}3 \le X < 5\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X < 3\text{{ or }}3 < X \le 5\}
4
A LaTex expression showing f(x) = \frac{square root of 1x-0}{1x+2}
What set describes the domain of this function?
a A LaTex expression showing \{X \in \mathbb{{R}} \vert 0 \le X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X \le 0\}
5
What set describes the domain of this function?
A LaTex expression showing f(x) = \frac{square root of 1x-5}{1x-5}
a A LaTex expression showing \{X \in \mathbb{{R}} \vert 5 < X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert -5 \le X \le 5\}
6
A LaTex expression showing f(x) = \frac{square root of 1x-3}{-1x-3}
What set describes the domain of this function?
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X \le 3\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert 3 \le X\}
7
What set describes the domain of this function?
A LaTex expression showing f(x) = \frac{square root of 1x+5}{-1x+3}
a A LaTex expression showing \{X \in \mathbb{{R}} \vert -5 \le X < 3\text{{ or }}3 < X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert -5 \le X \le 3\text{{ or }}-3 \le X \le 3\}
8
A LaTex expression showing f(x) = \frac{square root of 1x-5}{1x+1}
What set describes the domain of this function?
a A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert 5 \le X\}