This math topic focuses on identifying the domain of functions where the numerator is linear and the denominator is a quadratic equation that yields complex roots. It reinforces understanding how to deal with functions presented in a fraction format where the denominator affects the overall domain due to potential undefined behaviors (like division by zero). By presenting these functions and asking to determine their domains, learners enhance their problem-solving skills related to function properties and restrictions in real-number contexts.

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

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Function Domain - Fraction Linear over Quadratic (Complex Roots) to Domain Definition
1
A LaTex expression showing f(x) = 1x-4 over 1x to the power of 2 -1x+2
What set describes the domain of this function?
a A LaTex expression showing \{X \in \mathbb{{R}} \vert 1 \le X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
2
A LaTex expression showing f(x) = -1x-4 over 3x to the power of 2 -4x+22
What set describes the domain of this function?
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X \le 8\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
3
What set describes the domain of this function?
A LaTex expression showing f(x) = -1x+2 over 2x to the power of 2 -8x+22
a A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert -1 \le X\}
4
A LaTex expression showing f(x) = -1x+1 over -2x to the power of 2 -1x-17
What set describes the domain of this function?
a A LaTex expression showing \{X \in \mathbb{{R}} \vert 0 < X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
5
A LaTex expression showing f(x) = -1x-2 over 3x to the power of 2 -0x+24
What set describes the domain of this function?
a A LaTex expression showing \{ \}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
6
A LaTex expression showing f(x) = 1x-3 over 4x to the power of 2 +2x+10
What set describes the domain of this function?
a A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
b A LaTex expression showing \{ \}
7
A LaTex expression showing f(x) = -1x-5 over -4x to the power of 2 -8x-20
What set describes the domain of this function?
a A LaTex expression showing \{ \}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
8
A LaTex expression showing f(x) = -1x+3 over 5x to the power of 2 +5x+12
What set describes the domain of this function?
a A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
b A LaTex expression showing \{ \}