End Behavior of Polynomials

Front

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

Back

Degree 2 (quadratic)

Front

What is the end behavior of the polynomial function -1x^4 - 3x^3 + 3?

Back

As x approaches positive or negative infinity, the function approaches negative infinity.

Front

How is the end behavior of a polynomial function determined?

Back

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

Front

What is the leading coefficient and degree of the polynomial f(x) = -5x^7?

Back

Leading Coefficient: Negative, Degree: Odd.

Front

What is the degree classification of the polynomial x^2 + 4x - 8?

Back

Quadratic.

Front

What is the general form of a polynomial function?

Back

A polynomial function is expressed as f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n ≠ 0.

Front

What does it mean for a polynomial to have an even degree?

Back

A polynomial with an even degree will have the same end behavior on both sides (either both up or both down).

Front

What does it mean for a polynomial to have an odd degree?

Back

A polynomial with an odd degree will have opposite end behaviors (one side up and the other side down).

Front

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

Back

If the leading coefficient is positive, the ends of the graph will rise to the right; if negative, the ends will fall to the right.

Front

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

Back

Both ends of the graph will rise as x approaches positive and negative infinity.