Polynomial Functions: End Behavior; Number of possible Zeros

Front

What is a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n ≠ 0.

Front

What determines the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by its leading term, specifically the degree and the leading coefficient.

Front

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

Back

The end behavior is both ends of the graph rise upwards (Up ~ Up).

Front

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

Back

The end behavior is both ends of the graph fall downwards (Down ~ Down).

Front

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

Back

The end behavior is the left end falls down and the right end rises up (Down ~ Up).

Front

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

Back

The end behavior is the left end rises up and the right end falls down (Up ~ Down).

Front

How do you determine the number of possible zeros of a polynomial function?

Back

The number of possible zeros of a polynomial function is determined by its degree. A polynomial of degree n can have at most n real zeros.

Front

What is the Fundamental Theorem of Algebra?

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial function of degree n has exactly n roots in the complex number system, counting multiplicities.

Front

What is a zero of a polynomial function?

Back

A zero of a polynomial function is a value of x for which the function f(x) equals zero. It represents the x-intercepts of the graph.

Front

What is the relationship between the degree of a polynomial and the number of turning points?

Back

A polynomial function of degree n can have at most n-1 turning points.