How can the zeros degree and end behavior of a polynomial fu

How can the zeros, degree, and end behavior of a polynomial function allow a graph to be sketched?

Solution

To graph a polynomial function zeros,degree and end behaviour of a polynomial function are very usefull.

ZEROS: Zeros are nothing but the roots.Roots are x-values.Roots are the points where the graph crosses the x-axis..Therefore, By using zeros,the graph which crosses x-axis can be known.

DEGREE:Degree is the highest power of x.By using degree,one can know the turnings involved in the graph .The turnings are the spots where the graph turns back on itself and heads back the way.If a function has a degree \'n\' then no.of turnings will be atmost \'n-1\'.

END BEHAVIOUR: End behaviour can be used for the approach of \'x\'.To know the end behaviour,degree and leading coefficients are needed.Therefore, based on the deree and leading coefficient the end behaviour of a function i.e.,whether x is going towards positive infinite or negative infinite can be known.