polynomial functions

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 P(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where n is a non-negative integer.

Front

What is the degree of a polynomial function?

Back

The degree of a polynomial function is the highest power of the variable in the polynomial. It determines the polynomial's end behavior and the number of roots.

Front

How do you determine the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by the leading term (the term with the highest degree). If the leading coefficient is positive, the function rises to the right; if negative, it falls to the right.

Front

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

Back

The end behavior will be: as x → ∞, f(x) → ∞ and as x → -∞, f(x) → -∞.

Front

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

Back

The end behavior will be: as x → ∞, f(x) → ∞ and as x → -∞, f(x) → ∞.

Front

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

Back

The end behavior will be: as x → ∞, f(x) → -∞ and as x → -∞, f(x) → ∞.

Front

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

Back

The end behavior will be: as x → ∞, f(x) → -∞ and as x → -∞, f(x) → -∞.

Front

How can you identify the degree of a polynomial from its equation?

Back

To identify the degree of a polynomial, look for the term with the highest exponent of the variable. The exponent of that term is the degree of the polynomial.

Front

What is a leading coefficient in a polynomial function?

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.

Front

What does it mean for a polynomial to be even or odd?

Back

A polynomial is even if all its terms have even degrees, and it is odd if all its terms have odd degrees. This affects the symmetry of the graph.