End Behavior

Front

What is end behavior in the context of 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

Define the degree of a polynomial.

Back

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

Front

What does it mean if a polynomial function has an even degree?

Back

If a polynomial function has an even degree, its end behavior will be the same on both ends: as x approaches ±∞, f(x) approaches either +∞ or -∞.

Front

What does it mean if a polynomial function has an odd degree?

Back

If a polynomial function has an odd degree, its end behavior will be opposite on both ends: as x approaches -∞, f(x) approaches -∞, and as x approaches +∞, f(x) approaches +∞.

Front

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

Back

To determine the end behavior, look at the leading term of the polynomial. The sign and degree of the leading term dictate the behavior as x approaches ±∞.

Front

Back

Front

Back

Front

What does the notation @@f(x) ightarrow + ext{∞}@@ indicate?

Back

It indicates that the function f(x) increases without bound as x approaches a certain value.

Front

What does the notation @@f(x) ightarrow - ext{∞}@@ indicate?

Back

It indicates that the function f(x) decreases without bound as x approaches a certain value.

Front

How can you identify the leading term of a polynomial?

Back

The leading term is the term with the highest degree in the polynomial expression.