Question 1

Provide an appropriate response.
-What is the smallest possible degree of the function for which this graph represents?

A) 5
B) 2
C) 3
D) 4

Accepted Answer

The answer of Provide an appropriate response.
-What is the smallest...

Question 2

Provide an appropriate response.
-Why does a function defined by a polynomial of degree five with real coefficients have 
either 1, 3, or 5 real zeros counting multiplicities?

Accepted Answer

The answer of Provide an appropriate response.
-Why does a function...

Question 3

Provide an appropriate response.
-Why is it not possible for a function defined by a polynomial of degree 4 with real 
coefficients to have zeros of 2, 3, 5, and 1 + i?

Accepted Answer

The answer of Provide an appropriate response.
-Why is it not...

Question 4

Provide an appropriate response.
-What are the possible number of real zeros (counting multiplicities) for a polynomial 
function with real coefficients of degree four?

Accepted Answer

The answer of Provide an appropriate response.
-What are the possible...

Question 5

Provide an appropriate response.
-The domain of a polynomial function is the set of all real numbers. What is the range of a 
polynomial function of odd degree? One of even degree?

Accepted Answer

The answer of Provide an appropriate response.
-The domain of a...

Question 6

Provide an appropriate response.
-What is the domain of the graph?

A) $( - 8.85,44.86 )$
B) $( - 3.43,8.61 )$
C) $( - 8.85 , \infty )$
D) $( - \infty , \infty )$

Accepted Answer

The answer of Provide an appropriate response.
-What is the domain...

Question 7

Provide an appropriate response.
-What is the range of the graph? 
A) $( - 8.85,44.86 )$
B) $( - \infty , \infty )$
C) $( - 3.43,8.61 )$
D) $( - 8.85 , \infty )$

Accepted Answer

The answer of Provide an appropriate response.
-What is the range...

Question 8

Provide an appropriate response.
-What are the possible numbers of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree six?
A) 2, 4, or 6
B) 0, 2, 4, or 6
C) 6
D) 1, 3, or 5

Accepted Answer

A polynomial of degree n can have up to n real zeros (counting multiplicities), and by the Fundamental Theorem of Algebra, it must have exactly n roots (real or complex) in total. For a 6th degree polynomial, it can have 0, 2, 4, or 6 real zeros because complex roots occur in conjugate pairs. If there are complex roots, they reduce the number of real roots, but the total count of real and complex roots will always equal the degree of the polynomial.

Quiz 4: Polynomial and Rational Functions

Provide an appropriate response. -What is the smallest possible degree of the function for which this graph represents?

Provide an appropriate response. -Why does a function defined by a polynomial of degree five with real coefficients have either 1, 3, or 5 real zeros counting multiplicities?

Provide an appropriate response. -Why is it not possible for a function defined by a polynomial of degree 4 with real coefficients to have zeros of 2, 3, 5, and 1 + i?

Provide an appropriate response. -What are the possible number of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree four?

Provide an appropriate response. -The domain of a polynomial function is the set of all real numbers. What is the range of a polynomial function of odd degree? One of even degree?

Provide an appropriate response. -What is the domain of the graph? $Provide an appropriate response. -What is the domain of the graph? A) ( - 8.85,44.86 ) B) ( - 3.43,8.61 ) C) ( - 8.85 , \infty ) D) ( - \infty , \infty )$

Provide an appropriate response. -What is the range of the graph? $Provide an appropriate response. -What is the range of the graph? A) ( - 8.85,44.86 ) B) ( - \infty , \infty ) C) ( - 3.43,8.61 ) D) ( - 8.85 , \infty )$

Provide an appropriate response. -What are the possible numbers of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree six?