The graph of the function
$$f ( x ) = \frac { 3 x } { x + 1 }$$

is shown below. Determine the domain.

A) Domain: all real numbers except $x = - 1$
B) Domain: all real numbers except $x = - 1$ and $x = 0$
C) Domain: all real numbers except $x = - 1$ and $x = 3$
D) Domain: all real numbers except $x = 3$
E) Domain: all real numbers except $x = 0$

Question

The graph of the function
$$f ( x ) = \frac { 3 x } { x + 1 }$$

is shown below. Determine the domain.

A) Domain: all real numbers except $x = - 1$ 
B) Domain: all real numbers except $x = - 1$ and $x = 0$ 
C) Domain: all real numbers except $x = - 1$ and $x = 3$ 
D) Domain: all real numbers except $x = 3$ 
E) Domain: all real numbers except $x = 0$

Quizplus · Accepted Answer

The only restriction on the domain is that the denominator cannot be zero, which occurs only when $x=-1$. Thus, the domain is all real numbers except $x=-1$.

The Graph of the Function f(x)=3xx+1f ( x ) = \frac { 3 x } { x + 1 }f(x)=x+13x​

The Graph of the Function $f ( x ) = \frac { 3 x } { x + 1 }$