End Behavior and Multiplicity Practice

Front

What is the definition of multiplicity in the context of polynomial functions?

Back

Multiplicity refers to the number of times a particular root (or zero) appears in a polynomial function. A root with an odd multiplicity crosses the x-axis, while a root with an even multiplicity touches the x-axis.

Tags

CCSS.HSF-IF.C.7C

Front

What is the end behavior of a polynomial function with a positive leading coefficient and an even degree?

Back

The end behavior of such a polynomial function approaches positive infinity as x approaches both positive and negative infinity.

Front

What is the end behavior of a polynomial function with a negative leading coefficient and an odd degree?

Back

The end behavior of such a polynomial function approaches negative infinity as x approaches positive infinity and positive infinity as x approaches negative infinity.

Front

How does the multiplicity of a zero affect the graph of a polynomial function?

Back

A zero with an odd multiplicity will cross the x-axis, while a zero with an even multiplicity will touch the x-axis without crossing it.

Front

What is the multiplicity for the zero at x = 1?

Back

1

Tags

CCSS.HSF-IF.C.7C

Front

What is the multiplicity for the zero at x = -4?

Back

2

Tags

CCSS.HSF-IF.C.7C

Front

What is the multiplicity for the zero at x = 3?

Back

1

Tags

CCSS.HSF-IF.C.7C

Front

What is the end behavior of a polynomial function with a positive leading coefficient and an odd degree?

Back

The end behavior approaches positive infinity as x approaches positive infinity and negative infinity as x approaches negative infinity.

Front

What is the significance of the leading coefficient in determining the end behavior of a polynomial function?

Back

The leading coefficient determines the direction of the graph as x approaches positive or negative infinity, influencing whether the ends of the graph rise or fall.

Front

How can you determine the number of real roots of a polynomial function?

Back

The number of real roots can be determined by analyzing the degree of the polynomial and the multiplicities of its zeros.

Tags

CCSS.HSF-IF.C.7C