This topic focuses on finding the domain of functions that are represented as a ratio of an integer to a quadratic expression. The problems involve scenarios where the quadratic has complex roots. The main skill practiced here is identifying and expressing the set of all possible x-values (the domain) for which each function is defined. This involves understanding where the functions potentially have undefined points (due to zero denominators), and mathematically determining how to express those domains correctly using set notation.

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

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

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Function Domain - Fraction Integer over Quadratic (Complex Roots) to Domain Definition
1
What set describes the domain of this function?
A LaTex expression showing f(x) = 5 over 4x to the power of 2 +1x+4
a A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert -8 < X\}
2
What set describes the domain of this function?
A LaTex expression showing f(x) = -1 over 2x to the power of 2 -5x+10
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -6\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
3
A LaTex expression showing f(x) = 2 over 2x to the power of 2 +5x+13
What set describes the domain of this function?
a A LaTex expression showing \{ \}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
4
What set describes the domain of this function?
A LaTex expression showing f(x) = 4 over -4x to the power of 2 -1x-24
a A LaTex expression showing \{X \in \mathbb{{R}} \vert -9 \le X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
5
What set describes the domain of this function?
A LaTex expression showing f(x) = 3 over 4x to the power of 2 -8x+25
a A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert -7 \le X\}
6
A LaTex expression showing f(x) = -3 over -3x to the power of 2 -5x-10
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 X \le 0\}
7
What set describes the domain of this function?
A LaTex expression showing f(x) = -1 over 5x to the power of 2 +1x+21
a A LaTex expression showing \{X \in \mathbb{{R}} \vert -6 < X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
8
A LaTex expression showing f(x) = 5 over -5x 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 \}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert 3 < X\}