Best solutions to - "Determine whether the function is a polynomial function,..."

skomminbv

Answered question

2021-11-18

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 \times \frac{5}{2 x} + 1

Answer & Explanation

Whouldess

Beginner2021-11-19Added 11 answers

Step 1
We know,
A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable involved in the equation.
For example:

f (x) = x^{2} + 3 x + 4, g (x) = x + 16

.
Arational function is a function which is the ratio of two polynomial functions.
Arational function h(x) is of the following form,

= h (x) = \frac{f (x)}{g (x)}

,(where,

g (x) \neq 0

).
Now, given

f (x) = \frac{3 x^{3}}{2 x + 1}

It is the ratio of two polynomial functions.
hence

f (x) = \frac{3 x^{3}}{2 x + 1}

is a rational function.
Step 2
Result:

f (x) = \frac{3 x^{3}}{2 x + 1}

is rational function.

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