End Behavior

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

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

Back

As x → ∞, y → ∞ and as x → -∞, y → ∞.

Front

What does it mean when y → ∞ in terms of graph behavior?

Back

It means that the graph is rising towards positive infinity.

Front

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

Back

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

Front

Describe the end behavior of a polynomial with a positive leading coefficient and an odd degree.

Back

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

Front

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

Back

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

Front

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

Back

The degree determines whether the ends of the graph rise or fall as x approaches positive or negative infinity.

Front

What is the significance of the leading coefficient in determining end behavior?

Back

The sign of the leading coefficient indicates whether the graph will rise or fall at the ends.

Front

If a polynomial function's graph approaches y = 0 as x approaches -∞, what can be inferred about its end behavior?

Back

The graph is likely to have a leading coefficient that is positive and an even degree.

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 → -∞.