End Behavior of Polynomials

Front

What is the end behavior of a polynomial?

Back

The end behavior of a polynomial describes how the values of the polynomial behave as x approaches positive or negative infinity. It is determined by the leading term of the polynomial.

Front

What determines the end behavior of a polynomial function?

Back

The end behavior is determined by the leading term of the polynomial, specifically its degree and the sign of its leading coefficient.

Front

If a polynomial has an even degree and a positive leading coefficient, what is its end behavior?

Back

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

Front

If a polynomial has an even degree and a negative leading coefficient, what is its end behavior?

Back

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

Front

If a polynomial has an odd degree and a positive leading coefficient, what is its end behavior?

Back

As x approaches positive infinity, the polynomial approaches positive infinity, and as x approaches negative infinity, it approaches negative infinity.

Front

If a polynomial has an odd degree and a negative leading coefficient, what is its end behavior?

Back

As x approaches positive infinity, the polynomial approaches negative infinity, and as x approaches negative infinity, it approaches positive infinity.

Front

What is the leading term of the polynomial f(x) = 6x^3 - 7x^2 + 2x - 3?

Back

The leading term is 6x^3.

Front

How do you identify the end behavior of the polynomial g(x) = -3x^3 + 5x^2 + 4x + 8?

Back

Since the leading term is -3x^3 (odd degree, negative leading coefficient), as x approaches positive infinity, g(x) approaches negative infinity, and as x approaches negative infinity, g(x) approaches positive infinity.

Front

What is the end behavior of the polynomial f(x) = -7x^4 - 8x + 1?

Back

Since the leading term is -7x^4 (even degree, negative leading coefficient), as x approaches positive or negative infinity, f(x) approaches negative infinity.

Front

What is the end behavior of the linear polynomial y = -1/2x + 7?

Back

As x approaches positive or negative infinity, y approaches negative or positive infinity respectively, with a slope of -1/2.