This math topic focuses on determining the domain of square root functions, particularly involving quadratic expressions under the square root, which must yield non-negative values (real roots). The problems require the learners to identify the appropriate set of real numbers that describe where these functions are defined, based on the conditions derived from the quadratic expressions. Each question presents a function and multiple choice answers for the domain, testing the learners' understanding of function behavior and domain calculation. Overall, this involves applying knowledge of quadratic formulas, inequalities, and set notation to define valid x-values for the functions.

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Function Domain - Simple Root of Quadratic (Real Roots) to Domain Definition Worksheet

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