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 a negative leading coefficient indicate about the end behavior of a polynomial function?

Back

If a polynomial has a negative leading coefficient, the graph will fall to negative infinity as x approaches positive infinity.

Front

What does a positive leading coefficient indicate about the end behavior of a polynomial function?

Back

If a polynomial has a positive leading coefficient, the graph will rise to positive infinity as x approaches positive infinity.

Front

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

Back

The end behavior can be determined by the leading term of the polynomial, specifically the leading coefficient and the degree of the polynomial.

Front

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

Back

The end behavior will rise to positive infinity on both ends: as x approaches positive or negative infinity, y approaches positive infinity.

Front

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

Back

The end behavior will fall to negative infinity on both ends: as x approaches positive or negative infinity, y approaches negative infinity.

Front

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

Back

The end behavior will rise to positive infinity on the right and fall to negative infinity on the left: as x approaches positive infinity, y approaches positive infinity, and as x approaches negative infinity, y approaches negative infinity.

Front

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

Back

The end behavior will fall to negative infinity on the right and rise to positive infinity on the left: as x approaches positive infinity, y approaches negative infinity, and as x approaches negative infinity, y approaches positive infinity.

Front

What does the notation x→∞, y→∞ signify?

Back

It signifies that as x approaches positive infinity, the value of y also approaches positive infinity.

Front

What does the notation x→∞, y→0 signify?

Back

It signifies that as x approaches positive infinity, the value of y approaches zero.