U6D1 Polynomials End Behavior

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 the degree of the polynomial and the sign of the leading coefficient.

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 direction of the graph as x approaches positive or negative infinity.

Front

How does the degree of a polynomial affect its end behavior?

Back

If the degree is even, the ends of the graph will either both go up or both go down. If the degree is odd, one end will go up and the other will go down.

Front

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

Back

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

Front

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

Back

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

Front

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

Back

The end behavior is DOWN-UP; the left end falls while the right end rises.

Front

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

Back

The end behavior is UP-DOWN; the left end rises while the right end falls.

Front

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

Back

The leading coefficient is -3.

Front

Given f(x) = 4x^2 - 7x + 1, what is the degree of the polynomial?

Back

The degree of the polynomial is 2.