End Behavior

Front

What is end behavior in polynomial functions?

Back

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

Front

What does the leading coefficient determine in a polynomial function?

Back

The leading coefficient determines the direction of the graph's end behavior. If it is positive, the graph rises to the right; if negative, it falls to the right.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

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

Back

The degree determines whether the end behavior is even or odd. Even degrees have the same end behavior on both sides, while odd degrees have opposite end behaviors.

Front

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

Back

The end behavior is UP on both ends.

Front

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

Back

The end behavior is DOWN on both ends.

Front

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

Back

The end behavior is DOWN on the left and UP on the right.

Front

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

Back

The end behavior is UP on the left and DOWN on the right.

Front

How can you identify the end behavior of a polynomial function from its graph?

Back

You can identify the end behavior by observing the direction the graph approaches as x approaches positive and negative infinity.

Front

What is the significance of the leading term in a polynomial?

Back

The leading term, which includes the leading coefficient and the variable raised to the highest degree, primarily influences the end behavior of the polynomial.