End Behavior

Front

What is end behavior in the context of polynomial functions?

Back

End behavior describes how the values of a function behave as the input (x) approaches positive or negative infinity.

Front

What does it mean if a polynomial function's end behavior is described as x→∞, y→∞?

Back

It means that as x increases without bound, the value of the function (y) also increases without bound.

Front

What does it mean if a polynomial function's end behavior is described as x→-∞, y→-∞?

Back

It means that as x decreases without bound, the value of the function (y) also decreases without bound.

Front

How do you determine the end behavior of a polynomial function?

Back

The end behavior can be determined by the degree and leading coefficient of the polynomial.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

What is a leading coefficient?

Back

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

Front

What is the end behavior of a quartic polynomial with a positive leading coefficient?

Back

As x→∞, f(x)→∞ and as x→-∞, f(x)→∞.

Front

What is the end behavior of a cubic polynomial with a negative leading coefficient?

Back

As x→∞, f(x)→-∞ and as x→-∞, f(x)→∞.

Front

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

Back

As x→∞, f(x)→∞ and as x→-∞, f(x)→∞.

Front

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

Back

As x→∞, f(x)→-∞ and as x→-∞, f(x)→∞.