End Behavior

Front

What is End Behavior in mathematics?

Back

End Behavior refers to the behavior of a function as the input values (x) approach positive or negative infinity. It describes how the output values (y) behave in these limits.

Front

What does it mean if a function has end behavior of x→-∞, y→-∞?

Back

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

Front

What does it mean if a function has end behavior of x→∞, y→∞?

Back

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

Front

True or False: The end behavior of a function can be determined from its graph.

Back

True. The end behavior can often be observed by looking at the tails of the graph.

Front

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

Back

As x→-∞, y→∞ and x→∞, y→∞.

Front

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

Back

As x→-∞, y→-∞ and x→∞, y→∞.

Front

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

Back

As x→-∞, y→∞ and x→∞, y→-∞.

Front

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

Back

As x→-∞, y→-∞ and x→∞, y→-∞.

Front

How can you determine the end behavior of a rational function?

Back

Analyze the degrees of the numerator and denominator. The end behavior is influenced by the leading terms of both.

Front

What is the end behavior of the function f(x) = 1/x as x approaches infinity?

Back

As x→∞, y→0.