Understanding Polynomial Functions

This lesson covers the intercepts and turning points of polynomial functions, focusing on their short run behavior. It explains how the degree of a polynomial function determines the maximum number of x-intercepts and turns. Examples of degree 4 and degree 5 polynomials are provided, illustrating their intercepts and turning points. The lesson also discusses the end behavior of polynomials based on their degree and leading coefficient, highlighting differences between even and odd degree polynomials.

What is another term used to describe the intercepts and turning points of polynomial functions?

• Short run behavior

• Constant behavior

• Long run behavior

• Mid run behavior

Tags

CCSS.HSF-IF.C.7C

For a polynomial function of degree N, what is the maximum number of X intercepts it can have?

• N + 1

• 2N

• N - 1

• N

In a degree 4 polynomial function, what is the maximum number of turns it can have?

• 5

• 3

• 2

• 4

What happens to the graph of a polynomial function with an even degree and a positive leading coefficient as X approaches positive or negative infinity?

• The graph moves down

• The graph moves up

• The graph oscillates

• The graph remains constant

What is the behavior of the graph of a polynomial function with an even degree and a negative leading coefficient as X approaches negative infinity?

• The graph moves up

• The graph moves down

• The graph remains constant

• The graph oscillates

If a degree 5 polynomial function has 3 X intercepts and 2 turns, what might one incorrectly assume about its degree?

• It is a degree 6 polynomial

• It is a degree 3 polynomial

• It is a degree 4 polynomial

• It is a degree 2 polynomial

Tags

CCSS.HSF-IF.C.7C

How many X intercepts can a degree 5 polynomial function have at most?

• 6

• 5

• 4

• 3

What is the maximum number of turns a degree 5 polynomial function can have?

• 6

• 3

• 5

• 4

For an odd degree polynomial function with a negative leading coefficient, what is the end behavior as X approaches positive infinity?

• F of X approaches positive infinity

• F of X remains constant

• F of X approaches negative infinity

• F of X approaches zero

What is the end behavior of an odd degree polynomial function with a positive leading coefficient as X approaches negative infinity?

• F of X approaches zero

• F of X remains constant

• F of X approaches positive infinity

• F of X approaches negative infinity