Polynomial End Behavior

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

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.

Front

How do you determine the degree of a polynomial?

Back

The degree of a polynomial is determined by the highest exponent of the variable in the polynomial.

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as the input values approach positive or negative infinity.

Front

What factors determine the end behavior of a polynomial?

Back

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

Front

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

Back

The end behavior is UP-UP, meaning both ends of the graph rise as x approaches positive and negative infinity.

Front

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

Back

The end behavior is DOWN-DOWN, meaning both ends of the graph fall as x approaches positive and negative infinity.

Front

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

Back

The end behavior is DOWN-UP, meaning the left end of the graph falls and the right end rises.

Front

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

Back

The end behavior is UP-DOWN, meaning the left end of the graph rises and the right end falls.

Front

Given f(x) = 2x^3 + 4x - 5, what is the leading coefficient?

Back

The leading coefficient is 2.