End Behavior

Front

What is end behavior in the context of graphing functions?

Back

End behavior describes the behavior of the graph of a function as the input values (x) approach positive or negative infinity.

Front

How do you determine 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 does it mean if a polynomial has an odd degree and a positive leading coefficient?

Back

If a polynomial has an odd degree and a positive leading coefficient, the end behavior will be: as x → -∞, f(x) → -∞ and as x → +∞, f(x) → +∞.

Front

What does it mean if a polynomial has an even degree and a positive leading coefficient?

Back

If a polynomial has an even degree and a positive leading coefficient, the end behavior will be: as x → -∞, f(x) → +∞ and as x → +∞, f(x) → +∞.

Front

What does it mean if a polynomial has an odd degree and a negative leading coefficient?

Back

If a polynomial has an odd degree and a negative leading coefficient, the end behavior will be: as x → -∞, f(x) → +∞ and as x → +∞, f(x) → -∞.

Front

What does it mean if a polynomial has an even degree and a negative leading coefficient?

Back

If a polynomial has an even degree and a negative leading coefficient, the end behavior will be: as x → -∞, f(x) → -∞ and as x → +∞, f(x) → -∞.

Front

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

Back

The leading coefficient determines the direction of the graph's ends; whether they rise or fall as x approaches positive or negative infinity.

Front

How can you describe the end behavior of a function graphically?

Back

Graphically, end behavior can be described by observing the direction in which the graph heads as it moves towards the left and right ends of the coordinate plane.

Front

What is the end behavior of a polynomial function of degree 4 with a positive leading coefficient?

Back

For a polynomial function of degree 4 with a positive leading coefficient, the end behavior is: as x → -∞, f(x) → +∞ and as x → +∞, f(x) → +∞.

Front

What is the end behavior of a polynomial function of degree 3 with a negative leading coefficient?

Back

For a polynomial function of degree 3 with a negative leading coefficient, the end behavior is: as x → -∞, f(x) → +∞ and as x → +∞, f(x) → -∞.