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?

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A
Any real number
B
Positive numbers only
C
Negative numbers only

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Continuity

Polynomial functions are continuous over

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A
R
B
R-{0}
C
x>=0 only

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Range

The range of third degree polynomial function is always

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A
R
B
depends

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Range

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

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A
is R
B
it depends

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Number of zeros(roots)

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

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A
always two roots
B
always one root
C
less or equal to two roots
D
always no roots

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Number of zeros(roots)

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

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A
always three roots
B
always one root
C
at most three roots

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Number of zeros(roots)

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

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A
always four roots
B
always two roots
C
less or equal to four roots

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Number of turning points

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

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A
always 2
B
always 1
C
at least 2
D
at most 1

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The number of turning points

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

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A
always 1
B
always 2
C
less or equal to 2
D
more than 2

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Number of turning points

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

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A
always 4
B
always 3
C
more than 3
D
less or equal to 3

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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

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