End Behavior

Front

What is End Behavior in mathematics?

Back

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

Front

What does it mean when we say x→-∞ and y→-∞?

Back

It means that as x approaches negative infinity, the value of y also approaches negative infinity.

Front

What does it mean when we say x→∞ and y→∞?

Back

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

Front

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

Back

To determine the end behavior of a polynomial function, look at the leading term's degree and coefficient.

Front

What is the end behavior of the function f(x) = x^4 + 3x^3 - 4x + 1?

Back

As x→-∞, y→∞ and as x→∞, y→∞.

Front

What is the end behavior of the function f(x) = -x^2 - 3x + 1?

Back

As x→-∞, y→-∞ and as x→∞, y→-∞.

Front

What is the end behavior of the function f(x) = -x^3 + 2x^2 + 3?

Back

As x→-∞, y→∞ and as x→∞, y→-∞.

Front

What is the significance of arrows on a graph?

Back

Arrows indicate the direction in which the graph continues indefinitely, helping to determine end behavior.

Front

If a function has a positive leading coefficient and an even degree, what is its end behavior?

Back

As x→-∞, y→∞ and as x→∞, y→∞.

Front

If a function has a negative leading coefficient and an odd degree, what is its end behavior?

Back

As x→-∞, y→∞ and as x→∞, y→-∞.