Fill in the blank with one of the words or phrases listed below. Not all choices will be used. $$\begin{array} { l l l l }
\text { least common denominator } & \text { simplifying } & \text { reciprocals } & \text { numerator } \
\text { cross products } & \text { ratio } & \text { proportion } & \text { denominator } \
\text { rational expression } & \text { domain } & \text { complex fraction } & \
\frac { - a } { b } & \frac { a } { - b } & \frac { - a } { - b } &
\end{array}$$
-The _____of the rational function $f ( x ) = \frac { 1 } { x - 3 }$ is $\{ x \mid x$ is a real number, $x \neq 3 \}$.
A) complex fraction
B) denominator
C) domain
D) numerator

Question

Fill in the blank with one of the words or phrases listed below. Not all choices will be used. $$\begin{array} { l l l l } 
\text { least common denominator } & \text { simplifying } & \text { reciprocals } & \text { numerator } \
\text { cross products } & \text { ratio } & \text { proportion } & \text { denominator } \
\text { rational expression } & \text { domain } & \text { complex fraction } & \
\frac { - a } { b } & \frac { a } { - b } & \frac { - a } { - b } &
\end{array}$$
-The _____of the rational function $f ( x ) = \frac { 1 } { x - 3 }$ is $\{ x \mid x$ is a real number, $x \neq 3 \}$.
A) complex fraction
B) denominator
C) domain
D) numerator

Quizplus · Accepted Answer

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. In the case of $f(x) = \frac{1}{x-3}$, the function is undefined when $x-3 = 0$, or $x = 3$, because division by zero is undefined. Therefore, the domain is all real numbers except $x = 3$.

Fill in the Blank with One of the Words or Phrases