End Behavior of Functions

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity. It is determined by the leading term of the polynomial.

Front

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

Back

The degree of a polynomial determines the number of times the graph can turn and the direction in which it goes as x approaches infinity or negative infinity. Odd-degree polynomials have opposite end behaviors, while even-degree polynomials have the same end behavior.

Front

What is the leading coefficient test?

Back

The leading coefficient test helps determine the end behavior of a polynomial function based on the sign of the leading coefficient and the degree of the polynomial.

Front

For a polynomial of even degree with a positive leading coefficient, what is the end behavior?

Back

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

Front

For a polynomial of even degree with a negative leading coefficient, what is the end behavior?

Back

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

Front

For a polynomial of odd degree with a positive leading coefficient, what is the end behavior?

Back

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

Front

For a polynomial of odd degree with a negative leading coefficient, what is the end behavior?

Back

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

Front

What is the significance of the y-intercept in determining end behavior?

Back

The y-intercept provides a specific point on the graph but does not affect the end behavior, which is determined by the leading term.

Front

How can you determine the end behavior from a graph?

Back

To determine the end behavior from a graph, observe the direction in which the graph heads as x approaches -∞ and +∞.

Front

What is the end behavior of the function f(x) = 1 + x^4 - x^5 + 2x^2?

Back

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