SOLUTION: My teacher asks, "The difference between a polynomial or rational equation and polynomial or rational inequality"

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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(52824)   (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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