Polynomial End Behavior

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to whole number powers and coefficients, 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 power 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 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 either end: it will fall to the left and rise to the right or rise to the left and fall to the right.

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: it will either rise to both ends or fall to both ends.

Front

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

Back

If the leading coefficient is positive, the polynomial will rise to the right; if it is negative, the polynomial will fall to the right.

Front

What is the degree of the polynomial f(x) = 3x^2 - 4x + 1?

Back

The degree of the polynomial is 2 (quadratic).

Front

What is the leading coefficient of the polynomial f(x) = -7x^5 + 2x^3 - x + 4?

Back

The leading coefficient is -7.

Front

What is the end behavior of the polynomial f(x) = x^4 - 3x + 2?

Back

The end behavior is that it rises to both the left and the right.