document.write( "Question 511129: can the graph of a polynomial function have no y-intercepts? and no x-intercepts? \n" ); document.write( "

Algebra.Com's Answer #342011 by solver91311(24713) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "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

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-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.\r
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\n" ); document.write( "\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it
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$\"The$

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