SOLUTION: can the graph of a polynomial function have no y-intercepts? and no x-intercepts?
Algebra.Com
Question 511129: can the graph of a polynomial function have no y-intercepts? and no x-intercepts?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The domain of any polynomial function is the set of real numbers. Zero is a real number, therefore for any polynomial function 
, )
is defined and exists. The 
-intercept of a polynomial function is the point \right))
.
-intercepts of the graph of a polynomial function are points of the form )
where 
is a real number zero of the polynomial function. Since complex roots always occur in conjugate pairs, that is to say if 
is a root, then 
must also be a root, and the number of zeros of a polynomial function is equal to the degree of the function (Fundamental Theorem of Algebra) it is possible to have a polynomial function of even degree with no real number zeros, and therefore no -intercepts. Polynomial functions of odd degree are guaranteed to have at least one real zero and therefore at least one -intercept.
John
My calculator said it, I believe it, that settles it
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