HW 12 : Chapter 2.2 Homework (PC)

Front

What determines the end behavior of a polynomial function?

Back

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

Front

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

Back

The leading coefficient affects the direction in which the graph of the polynomial function rises or falls as x approaches positive or negative infinity.

Front

What does an even degree polynomial with a positive leading coefficient look like?

Back

As x approaches positive or negative infinity, the graph rises in both directions.

Front

What does an odd degree polynomial with a negative leading coefficient look like?

Back

As x approaches positive infinity, the graph falls, and as x approaches negative infinity, the graph rises.

Front

What is a zero of a polynomial function?

Back

A zero of a polynomial function is a value of x for which the polynomial evaluates to zero.

Front

How can you determine the number of zeros a polynomial function has?

Back

The number of zeros can be determined by the degree of the polynomial, which indicates the maximum number of real zeros.

Front

What does the Fundamental Theorem of Algebra state?

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial function has at least one complex root.

Front

What is the relationship between the degree of a polynomial and its end behavior?

Back

The degree of a polynomial indicates the number of times the graph can change direction, affecting its end behavior.

Front

What is the significance of a polynomial having a zero at x = -3?

Back

If a polynomial has a zero at x = -3, it means that the graph intersects the x-axis at that point.

Front

What does it mean if a polynomial has a double root?

Back

A double root means that the polynomial touches the x-axis at that root but does not cross it.