A polynomial is a group or a collection of terms added or subtracted together each of which have exponents that are positive integers. Let’s say f(x) =4 or f(x) =3x or f(x) =5x^2+x-7 all of these terms have the positive integers. A non-polynomial example would be f(x) = 2/x^3 which is nothing but 2x^-3, here the exponent is in negative integer hence it’s a non-polynomial. On Graph the polynomial functions are never sharp; in fact they are smooth with no breaks in them. If we are attempting to graph a polynomial function then Let’s start with an example F(x) =(x-1)(x-2)(x+4) ,
when we look at the mathematicspolynomial function we want to know that what would be the end behavior.as we approach negative infinity what will happen to the graph or as we approach positive infinity what will happen to the graph. Where to find the end of behavior if we do not know what is our degree. As we look at the equation, x time x times x =x^3.thus the degree of polynomial is 3 or N=3. Now let’s find the coefficient of the three terms is 1 we also call it as a of n is 1 >0. Based on degree and the coefficient, our negative infinity and out positive infinity will be approached.
Next step would be maximum number of turns. It’s just taking degree and subtracting one from it that is n-1, which is 3-1=2. After finding the end behavior and max number, next we will find the y intercepts. In this we put o instead of x that is f(0)=(0-1)(0-2)(0+4) ,we simplify getting (-1) (-2)(4)=8. Thus our y – intercepts is (0, 8).Next step would be finding x intercepts or zero. This way using the polynomial function (x-1)=0,(x-2)=0 and (x+4)=0.here we get as x=1,x=2 and x=-4. This way we will hit on x axis (1, 0), (2,0) and (-4,0) on the graph.
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