Give the domain and range for the rational function. Use interval notation.
-$$f ( x ) = \frac { 1 } { ( x - 3 ) ^ { 2 } } + 5$$
A) Domain: $( - \infty , 5 ) \cup ( 5 , \infty )$; Range: $( 0 , \infty )$
B) Domain: $( - \infty , - 3 ) \cup ( - 3 , \infty )$; Range: $( - \infty , 5 )$
C) Domain: $( - \infty , 3 ) \cup ( 3 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$
D) Domain: $( - \infty , 3 ) \cup ( 3 , \infty )$; Range: $( 5 , \infty )$

Question

Quizplus · Accepted Answer

The function is undefined at $x = 3$, so the domain excludes 3. The range is all values greater than 5 because the smallest value of the function occurs when the denominator is largest, which approaches but never reaches 0, thus the function approaches but never reaches 5, only exceeding it.

Give the Domain and Range for the Rational Function f(x)=1(x−3)2+5f ( x ) = \frac { 1 } { ( x - 3 ) ^ { 2 } } + 5f(x)=(x−3)21​+5

Give the Domain and Range for the Rational Function $f ( x ) = \frac { 1 } { ( x - 3 ) ^ { 2 } } + 5$