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?

Select all that apply

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

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Continuity

Polynomial functions are continuous over

Select all that apply

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

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Range

The range of third degree polynomial function is always

Select all that apply

A
R
B
depends

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Range

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

Select all that apply

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)

Select all that apply

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)

Select all that apply

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)

Select all that apply

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

Select all that apply

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

Select all that apply

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

Select all that apply

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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