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 has a leading coefficient that is positive and an even degree?

Back

The graph will rise to positive infinity on both ends as x approaches positive and negative infinity.

Front

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

Back

The graph will fall to negative infinity on both ends as x approaches positive and negative infinity.

Front

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

Back

The graph will rise to positive infinity as x approaches positive infinity and fall to negative infinity as x approaches negative infinity.

Front

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

Back

The graph will fall to negative infinity as x approaches positive infinity and rise to positive infinity as x approaches negative infinity.

Front

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

Back

Observe the direction in which the graph heads as x approaches positive and negative infinity.

Front

What is the significance of the degree of a polynomial in determining its end behavior?

Back

The degree indicates the highest power of x, which influences whether the ends of the graph rise or fall.

Front

If a polynomial function has a degree of 4, what can you infer about its end behavior?

Back

If the leading coefficient is positive, the ends will rise; if negative, the ends will fall.

Front

What is the end behavior of the function f(x) = x^2?

Back

As x approaches ±∞, f(x) approaches +∞.

Front

What is the end behavior of the function f(x) = -x^3?

Back

As x approaches +∞, f(x) approaches -∞; as x approaches -∞, f(x) approaches +∞.