3.1-3.3 Review Honors Pre-Calculus (Polynomial Functions)

Front

What is the interval where a polynomial function is decreasing?

Back

The function is decreasing on the intervals (−∞, −2.55) U (0, 2.55).

Front

How is the end behavior of a polynomial function determined?

Back

The end behavior is determined by the degree and the sign of the leading coefficient.

Front

What does it mean if a zero has even multiplicity?

Back

A zero has even multiplicity if the graph touches the x-axis at that zero but does not cross it.

Front

What does it mean if a zero has odd multiplicity?

Back

A zero has odd multiplicity if the graph crosses the x-axis at that zero.

Front

Identify the degree and leading coefficient sign for the polynomial: -2x^7 + 2x^4 + 4.

Back

Degree: 7 (Odd), Leading Coefficient: Negative.

Front

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

Back

The leading coefficient determines the direction of the graph's end behavior.

Front

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

Back

The ends of the graph rise in both directions.

Front

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

Back

The left end of the graph rises and the right end falls.

Front

How can you determine the multiplicity of a zero from a polynomial function?

Back

By examining the factors of the polynomial; if a factor is squared, it indicates even multiplicity.

Front

What is the relationship between the degree of a polynomial and the number of zeros it can have?

Back

A polynomial of degree n can have up to n zeros.