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 has a positive leading coefficient?

Back

If a polynomial function has a positive leading coefficient, the graph will rise to positive infinity as x approaches positive infinity.

Front

What does it mean if a polynomial function has a negative leading coefficient?

Back

If a polynomial function has a negative leading coefficient, the graph will fall to negative infinity as x approaches positive infinity.

Front

Describe the end behavior of a quartic polynomial with a positive leading coefficient.

Back

As x → ∞, y → ∞ and as x → -∞, y → ∞.

Front

Describe the end behavior of a cubic polynomial with a negative leading coefficient.

Back

As x → ∞, y → -∞ and as x → -∞, y → ∞.

Front

What does it indicate if a function goes up on the left side of the graph?

Back

It indicates that as x approaches negative infinity (x → -∞), y approaches positive infinity (y → ∞).

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

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

Back

You can determine the end behavior by looking at the degree and the leading coefficient of the polynomial.

Front

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

Back

As x → ∞, y → -∞ and as x → -∞, y → -∞.

Front

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

Back

As x → ∞, y → ∞ and as x → -∞, y → -∞.