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Question 1153658: My teacher asks, "The difference between a polynomial or rational equation and polynomial or rational inequality"
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52817)   (Show Source):
You can put this solution on YOUR website! .
An equation has the EQUALITY sign " = " between two parts (between two expressions).
An inequality has the INEQUALITY sign " < ", or " <= ", or " > ", or " >= " between two parts (between two expressions).
Happy learning (!)
Answer by MathLover1(20850)  (Show Source):
You can put this solution on YOUR website! The difference between a polynomial or rational equation and polynomial or rational inequality:
An equation has the EQUALITY sign " = " between two parts (between two expressions).
A polynomial function is a function of the form:
 +....+ where  is a non-negative integer and 
A polynomial of degree  has at most real zeros and  turning points.
The difference between a polynomial or rational equation and polynomial or rational inequality:
A polynomial function is a function of the form:
+....+ where is a non-negative integer and
A polynomial of degree has at most real zeros and turning points.
First, the end behavior of a polynomial is determined by its  and the  of the   .
The degree of a polynomial function determines the end behavior of its graph. If the degree of a polynomial is even, then the end behavior is the same in both directions. If the degree of a polynomial is odd, then the end behavior on the left is the opposite of the behavior on the right.
A rational equation is just a quotient of two polynomials. Quotient here just means “fraction.” So, if  is a rational expression, then it can be written as:
 where  and  are both polynomials.
A rational function may have a  asymptote whenever  which  the  of the function.
The graphs of rational functions may have vertical asymptotes only where the denominator is zero, and a  asymptote (a horizontal line that the graph approaches as the input increases or decreases without bound).
The end behavior of the graph of a rational function is determined by the  of the  in the  and  .
The graphs of rational functions may have vertical asymptotes only where the denominator is zero.
Two differences difference between a  or  :
First, an inequality has the INEQUALITY sign " < ", or " <= ", or " > ", or " >= " between two parts (between two expressions).
A polynomial inequality (PI) can  be replaced by a PI with one side zero. That is, is the same as  .
A rational inequality (RI)   , because you   the  of the ;
 can not safely be replaced by
because  and/or  might change signs unexpectedly.
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