Behavior of polynomial function
Start from second degree polynomials and then third degree...
Change the parameters a, b, c, d, and e many times to check the following
1) What are the general characteristics of polynomial functions (Domain, range, continuity...)
2) The zeros of polynomial functions (their number, relation to the degree...)
3) The number of maximum, minimums, turning points with respect to the degree
At the end answer the questions below
Polynomial functions
Domain
The domain of any polynomial function is?
Continuity
Polynomial functions are continuous over
Range
The range of third degree polynomial function is always
Range
The range of polynomial function with 2nd or 4th degree
Number of zeros(roots)
The number of real roots (the x-intercepts) of a second degree is (are)
Number of zeros(roots)
The number of real roots (the x-intercepts) of a third degree is (are)
Number of zeros(roots)
The number of real roots (the x-intercepts) of a fourth degree is (are)
Number of turning points
The number of turning points (max-min) of a second degree polynomial is/are
The number of turning points
The number of turning points (max-min) of a third degree polynomial is/are
Number of turning points
The number of turning points (max-min) of a fourth degree polynomial is/are