Asked by Charlene Coleman on Jun 13, 2024
Verified
Find the domain of the rational function. f(x) =9x−5f ( x ) = \frac { 9 } { x - 5 }f(x) =x−59
A) (−∞,5) ∪(5,∞) ( - \infty , 5 ) \cup ( 5 , \infty ) (−∞,5) ∪(5,∞)
B) (−∞,9) ∪(9,∞) ( - \infty , 9 ) \cup ( 9 , \infty ) (−∞,9) ∪(9,∞)
C) (−∞,−5) ∪(−5,5) ∪(5,∞) ( - \infty , - 5 ) \cup ( - 5,5 ) \cup ( 5 , \infty ) (−∞,−5) ∪(−5,5) ∪(5,∞)
D) (−∞,∞) ( - \infty , \infty ) (−∞,∞)
E) (−∞,5) ∪(5,9) ∪(9,∞) ( - \infty , 5 ) \cup ( 5,9 ) \cup ( 9 , \infty ) (−∞,5) ∪(5,9) ∪(9,∞)
Domain
The set of all possible input values (x-values) for which a given function is defined.
Rational Function
A function characterized by the ratio of two polynomials.
- Distinguish and explain the domain of rational functions.
Verified Answer
KR
Katie RannoJun 14, 2024
Final Answer :
A
Explanation :
The denominator cannot be equal to zero, so the function is undefined at $x = 5$. Therefore, the domain is all real numbers except $5$, which is represented by the interval notation $( - \infty , 5 ) \cup ( 5 , \infty )$.
Learning Objectives
- Distinguish and explain the domain of rational functions.