Give the domain and range for the rational function. Use interval notation.
-$$f ( x ) = \frac { 3 } { x }$$
A) Domain: $( - \infty , 3 ) \cup ( 3 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$
B) Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$
C) Domain: $( - \infty , 3 ) \cup ( 3 , \infty )$; Range: $( 0 , \infty )$
D) Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( 0 , \infty )$

Question

Quizplus · Accepted Answer

The function $f(x) = \frac{3}{x}$ is undefined at $x = 0$, so the domain excludes 0, making it $(-\infty, 0) \cup (0, \infty)$. The range is also $(-\infty, 0) \cup (0, \infty)$ because as $x$ approaches 0 from the positive side, $f(x)$ approaches $\infty$, and as $x$ approaches 0 from the negative side, $f(x)$ approaches $-\infty$, but it can never actually be 0.

Give the Domain and Range for the Rational Function f(x)=3xf ( x ) = \frac { 3 } { x }f(x)=x3​

Give the Domain and Range for the Rational Function $f ( x ) = \frac { 3 } { x }$