Determine the domain and the range. $g ( x ) = \frac { 11 x - 20 } { 3 x - 18 }$
A) domain: $\left( - \infty , \frac { 11 } { 3 } \right) \cup \left( \frac { 11 } { 3 } , \infty \right)$ range: $( - \infty , 6 ) \cup ( 6 , \infty )$ ;
B) domain: $( - \infty , 6 ) \cup ( 6 , \infty )$ ; range: $\left( - \infty , \frac { 20 } { 11 } \right) \cup \left( \frac { 20 } { 11 } , \infty \right)$
C) domain: $( - \infty , 6 ) \cup ( 6 , \infty )$ ; range: $\left( - \infty , \frac { 11 } { 3 } \right) \cup \left( \frac { 11 } { 3 } , \infty \right)$
D) domain: $( - \infty , 6 ) \cup ( 6 , \infty )$ ; range: $\left( - \infty , \frac { 3 } { 11 } \right) \cup \left( \frac { 3 } { 11 } , \infty \right)$
E) domain: $( - \infty , 6 ) \cup ( 6 , \infty )$ ; range: $\left( - \infty , \frac { 11 } { 18 } \right) \cup \left( \frac { 11 } { 18 } , \infty \right)$

Question

Quizplus · Accepted Answer

The domain is determined by the values of $x$ that make the denominator non-zero. We have $3x-18=3(x-6)=0$ when $x=6,$ so $x
eq 6$ for the function to be defined. Thus, the domain is $(-\infty,6)\cup(6,\infty).$

To find the range, we note that as $x$ approaches $\frac{6}{3}=2$ from the left, $g(x)$ approaches negative infinity while as $x$ approaches $2$ from the right, $g(x)$ approaches positive infinity. Similarly, as $x$ approaches $+\infty,$ $g(x)$ approaches $\frac{11}{3}$ from above, while as $x$ approaches $-\infty,$ $g(x)$ approaches $-\frac{11}{3}$ from below. Thus, the range is $\left(-\infty,\frac{11}{3}ight)\cup\left(\frac{11}{3},+\inftyight).$

Determine the Domain and the Range g(x)=11x−203x−18g ( x ) = \frac { 11 x - 20 } { 3 x - 18 }g(x)=3x−1811x−20​

Determine the Domain and the Range $g ( x ) = \frac { 11 x - 20 } { 3 x - 18 }$