Asked by Swakena Jackson on May 21, 2024
Verified
Find the domain of the rational function. f(x) =x2+46f ( x ) = \frac { x ^ { 2 } + 4 } { 6 }f(x) =6x2+4
A) (−∞,∞) ( - \infty , \infty ) (−∞,∞)
B) (−∞,4) ∪(4,6) ∪(6,∞) ( - \infty , 4 ) \cup ( 4,6 ) \cup ( 6 , \infty ) (−∞,4) ∪(4,6) ∪(6,∞)
C) (−∞,−4) ∪(−4,4) ∪(4,∞) ( - \infty , - 4 ) \cup ( - 4,4 ) \cup ( 4 , \infty ) (−∞,−4) ∪(−4,4) ∪(4,∞)
D) (−∞,6) ∪(6,∞) ( - \infty , 6 ) \cup ( 6 , \infty ) (−∞,6) ∪(6,∞)
E) (−∞,4) ∪(4,∞) ( - \infty , 4 ) \cup ( 4 , \infty ) (−∞,4) ∪(4,∞)
Domain
In mathematics, the set of all possible input values for which a function is defined.
Rational Function
A function represented by the ratio of two polynomials, where the denominator is not zero.
- Detect and expound upon the domain of rational functions.
Verified Answer
DK
Dennell KrebsMay 27, 2024
Final Answer :
A
Explanation :
The given rational function is defined for all real numbers because the denominator is a constant and never equals zero. Therefore, the domain of the function is all real numbers, which is represented by choice A.
Learning Objectives
- Detect and expound upon the domain of rational functions.