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

If the degree is even, both ends of the graph will either rise or fall together. If the degree is odd, one end will rise while the other falls.

Front

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

Back

Both ends of the graph will rise as x approaches positive or negative infinity.

Front

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

Back

Both ends of the graph will fall as x approaches positive or negative infinity.

Front

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

Back

The left end of the graph will fall while the right end will rise as x approaches negative and positive infinity, respectively.

Front

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

Back

The left end of the graph will rise while the right end will fall as x approaches negative and positive infinity, respectively.

Front

Identify the end behavior of the function: f(x) = -x^2 - 3x + 1.

Back

DOWN, DOWN (both ends fall).

Front

Identify the end behavior of the function: f(x) = 3x^8 + 3x^5 - 4x + 7.

Back

UP, UP (both ends rise).