Module 3 Polynomial Functions Review CP

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity. It is determined by the degree and leading coefficient of the polynomial.

Front

Define increasing and decreasing intervals in a graph.

Back

Increasing intervals are ranges of x-values where the function's output (y-value) is rising. Decreasing intervals are ranges where the function's output is falling.

Front

What does it mean if a polynomial function has an odd degree?

Back

A polynomial function with an odd degree will have opposite end behaviors; as x approaches positive infinity, f(x) approaches positive infinity, and as x approaches negative infinity, f(x) approaches negative infinity.

Front

What does it mean if a polynomial function has a positive leading coefficient?

Back

A polynomial function with a positive leading coefficient will rise to positive infinity as x approaches positive infinity.

Front

What is factored form of a polynomial?

Back

Factored form expresses a polynomial as a product of its linear factors, which can help identify the roots of the function.

Front

How do you find the local maximum of a function?

Back

The local maximum of a function is the highest point in a specific interval. It can be found using calculus (derivatives) or by analyzing the graph.

Front

What is the significance of the roots of a polynomial function?

Back

The roots (or zeros) of a polynomial function are the x-values where the function equals zero. They represent the points where the graph intersects the x-axis.

Front

Explain the concept of multiplicity in polynomial roots.

Back

Multiplicity refers to the number of times a particular root appears in a polynomial. A root with an even multiplicity will touch the x-axis, while a root with an odd multiplicity will cross it.

Front

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

Back

The degree of a polynomial indicates the maximum number of roots it can have. For example, a polynomial of degree n can have up to n roots.

Front

What is the difference between a local maximum and a global maximum?

Back

A local maximum is the highest point in a specific interval, while a global maximum is the highest point over the entire domain of the function.