# Are all polynomials rational functions? Are all algebraic functions polynomials?

Question
Rational functions
Are all polynomials rational functions? Are all algebraic functions polynomials?

2020-11-07
It is known that all polynomials are not rational functions.
Example:
Consider the function $$f(x)=pi$$. This, function is a polynomial but it cannot be written in the form of a rational function.
Hence, all polynomials are not rational functions.
Step 2
No, not all algebraic functions are polynomials.
If an algebraic expression has a radical, then it cannot be a polynomial.

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Step 1
Calculus homework question answer, step 1, image 1
Step 2
Calculus homework question answer, step 2, image 1
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