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 it mean if a polynomial has an odd degree?

Back

If a polynomial has an odd degree, its end behavior will go in opposite directions: as x approaches negative infinity, the function approaches negative infinity, and as x approaches positive infinity, the function approaches positive infinity.

Front

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

Back

If a polynomial has an even degree, its end behavior will go in the same direction: as x approaches both positive and negative infinity, the function approaches either positive or negative infinity.

Front

How does the leading coefficient affect end behavior?

Back

The sign of the leading coefficient determines the direction of the end behavior: a positive leading coefficient means the ends of the graph will rise, while a negative leading coefficient means the ends will fall.

Front

Back

The leading coefficient is 7.

Front

Back

The degree of the polynomial is 5.

Front

Back

The end behavior is Down/UP.

Front

Back

The end behavior is Up/Down.

Front

What does @@x ightarrow - ext{infinity}@@ represent?

Back

It represents the left end of the graph as x approaches negative infinity.

Front

What does @@x ightarrow ext{infinity}@@ represent?

Back

It represents the right end of the graph as x approaches positive infinity.