Give the domain and range for the rational function. Use interval notation.
-$$f ( x ) = \frac { 2 } { x } + 3$$
A) Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( - \infty , 3 ) \cup ( 3 , \infty )$
B) Domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; Range: $( - \infty , 3 ) \cup ( 3 , \infty )$
C) Domain: $( - \infty , 3 ) \cup ( 3 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$
D) Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( - \infty , - 3 ) \cup ( - 3 , \infty )$

Question

Quizplus · Accepted Answer

The domain of $f(x) = \frac{2}{x} + 3$ excludes $x = 0$ because division by zero is undefined, hence $( - \infty , 0 ) \cup ( 0 , \infty )$. The range is all real numbers except for 3, as the function approaches but never reaches a value of 3, making the correct range $( - \infty , \infty )$, but since no option matches this exact description, the closest correct interpretation based on the provided options would be a misunderstanding in the interpretation of the range. The function can actually take on values less than and greater than 3, so the initial explanation for the range was incorrect. The function's range is indeed all real numbers, as the value of $f(x)$ can be made arbitrarily large or small by choosing appropriate values of $x$.

Give the Domain and Range for the Rational Function f(x)=2x+3f ( x ) = \frac { 2 } { x } + 3f(x)=x2​+3

Give the Domain and Range for the Rational Function $f ( x ) = \frac { 2 } { x } + 3$