Behavior of polynomial function

Start from second degree polynomials and then third degree...[br]Change the parameters a, b, c, d, and e many times to check the following [br][br]1) What are the general characteristics of polynomial functions (Domain, range, continuity...)[br]2) The zeros of polynomial functions (their number, relation to the degree...)[br]3) The number of maximum, minimums, turning points with respect to the degree[br][br]At the end answer the questions below

Polynomial functions

Domain

The domain of any polynomial function is?

Any real number Negative numbers only Positive numbers only

Continuity

Polynomial functions are continuous over

x>=0 only R R-{0}

Range

The range of third degree polynomial function is always

depends R

Range

The range of polynomial function with 2nd or 4th degree

it depends is R

Number of zeros(roots)

The number of real roots (the x-intercepts) of a second degree is (are)

always two roots always no roots less or equal to two roots always one root

Number of zeros(roots)

The number of real roots (the x-intercepts) of a third degree is (are)

at most three roots always one root always three roots

Number of zeros(roots)

The number of real roots (the x-intercepts) of a fourth degree is (are)

less or equal to four roots always four roots always two roots

Number of turning points

The number of turning points (max-min) of a second degree polynomial is/are

always 1 at least 2 always 2 at most 1

The number of turning points

The number of turning points (max-min) of a third degree polynomial is/are

always 2 less or equal to 2 always 1 more than 2

Number of turning points

The number of turning points (max-min) of a fourth degree polynomial is/are

more than 3 always 4 less or equal to 3 always 3

Behavior of polynomial function

Polynomial functions

Domain

Continuity

Range

Range

Number of zeros(roots)

Number of zeros(roots)

Number of zeros(roots)

Number of turning points

The number of turning points

Number of turning points

Information: Behavior of polynomial function