In Problems 1 − 4 , determine whether the function is a polynomial function, a rational function, or neither. For those that are polynomial functions, state the degree. For those that are not polynomial functions, tell why not. f ( x ) = 3 x 5 2 x + 1
In Problems 1 − 4 , determine whether the function is a polynomial function, a rational function, or neither. For those that are polynomial functions, state the degree. For those that are not polynomial functions, tell why not. f ( x ) = 3 x 5 2 x + 1
Solution Summary: The author explains that the function f(x)=3x52x+1 is a rational function and not polynomial.
In Problems
1
−
4
, determine whether the function is a polynomial function, a rational function, or neither. For those that are polynomial functions, state the degree. For those that are not polynomial functions, tell why not.
f
(
x
)
=
3
x
5
2
x
+
1
Expert Solution & Answer
To determine
Whether the function f(x)=3x52x+1 is a polynomial function, a rational function, or neither. If polynomial, state degree, otherwise tell why not.
Answer to Problem 2RE
Solution:
The function f(x)=3x52x+1 is a rational function and not polynomial function since it is ratio of two polynomials.
Explanation of Solution
Given Information:
The function, f(x)=3x52x+1
The rational function is of the form R(x)=p(x)q(x) where p and q are polynomial functions and q is not zero polynomial.
In a function 3x5 and 2x+1 are polynomial functions and 2x+1 is not the zero polynomial.
Hence, the function f(x)=3x52x+1 is a rational function.
It is not polynomial function since it is ratio of two polynomials.
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