3.2 Pt.1 Polynomial Functions Practice

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 does the degree of a polynomial indicate?

Back

The degree of a polynomial indicates the highest power of the variable in the polynomial. It determines the polynomial's end behavior and the number of real zeros.

Front

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

Back

The number of real zeros can be determined by analyzing the degree of the polynomial and using the Fundamental Theorem of Algebra, which states that a polynomial of degree n has exactly n roots (real or complex).

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It influences the end behavior of the polynomial function.

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 the sign of the leading coefficient.

Front

What does it mean if a polynomial has an even degree?

Back

If a polynomial has an even degree, its end behavior will be the same on both ends: both will approach +∞ or both will approach -∞.

Front

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

Back

If a polynomial has an odd degree, its end behavior will be opposite on both ends: one end will approach +∞ and the other will approach -∞.

Front

How does the sign of the leading coefficient affect the end behavior of a polynomial?

Back

If the leading coefficient is positive, the polynomial will approach +∞ as x approaches +∞ and -∞ as x approaches -∞ for odd degrees. For even degrees, it will approach +∞ on both ends. If negative, the behavior is reversed.

Front

What is the difference between a polynomial with a positive leading coefficient and one with a negative leading coefficient?

Back

A polynomial with a positive leading coefficient will rise to +∞ on the right end, while one with a negative leading coefficient will fall to -∞ on the right end.

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. It represents the x-intercepts of the graph.