End Behavior

Front

What does x → -∞ mean?

Back

It indicates that the value of x is approaching negative infinity, or moving left on the x-axis.

Front

What does x → ∞ mean?

Back

It indicates that the value of x is approaching positive infinity, or moving right on the x-axis.

Front

What is end behavior in the context of polynomial functions?

Back

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

Front

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

Back

The degree determines the direction of the ends of the graph; even degrees have both ends going in the same direction, while odd degrees have ends going in opposite directions.

Front

What does a positive leading coefficient indicate about the end behavior of a polynomial?

Back

If the leading coefficient is positive, the graph will rise to positive infinity as x approaches positive infinity.

Front

What does a negative leading coefficient indicate about the end behavior of a polynomial?

Back

If the leading coefficient is negative, the graph will fall to negative infinity as x approaches positive infinity.

Front

What is the end behavior of the polynomial f(x) = x^4 + 3x^3 - 4x + 1?

Back

As x → ∞, y → ∞ and as x → -∞, y → ∞.

Front

What is the end behavior of the polynomial f(x) = -x^2 - 3x + 1?

Back

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

Front

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

Back

The graph will fall to negative infinity on both ends: as x → ∞, y → -∞ and as x → -∞, y → -∞.

Front

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

Back

The graph will rise to positive infinity on the right and fall to negative infinity on the left: as x → ∞, y → ∞ and as x → -∞, y → -∞.