3.3.4 End Behavior and Multiplicity

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

Back

As x approaches positive or negative infinity, f(x) approaches positive infinity.

Front

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

Back

As x approaches positive or negative infinity, f(x) approaches negative infinity.

Front

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

Back

As x approaches positive infinity, f(x) approaches positive infinity, and as x approaches negative infinity, f(x) approaches negative infinity.

Front

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

Back

As x approaches positive infinity, f(x) approaches negative infinity, and as x approaches negative infinity, f(x) approaches positive infinity.

Front

Define 'leading coefficient' in a polynomial function.

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

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

Back

The degree of the polynomial is 5.

Front

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

Back

The degree determines whether the ends of the graph go in the same direction (even degree) or in opposite directions (odd degree).

Front

What is the leading coefficient of the polynomial f(x) = -2x^7 + 3x^4 - 1?

Back

The leading coefficient is -2.

Front

Identify the end behavior of the polynomial f(x) = 3x^8 + 2x^3 - 5.

Back

As x approaches positive or negative infinity, f(x) approaches positive infinity.