End Behavior

Front

What is end behavior in the context of functions?

Back

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

Front

What does it mean if a function's end behavior is x→-∞, y→-∞?

Back

It means that as x approaches negative infinity, the function's output (y) also approaches negative infinity, indicating the graph falls to the left.

Front

What does it mean if a function's end behavior is x→∞, y→∞?

Back

It means that as x approaches positive infinity, the function's output (y) approaches positive infinity, indicating the graph rises to the right.

Front

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

Back

The end behavior of a polynomial function is determined by its leading term. For example, in f(x) = ax^n, if a > 0 and n is even, both ends of the graph rise.

Front

What is the end behavior of the function f(x) = 3x^4 + 2x - 5?

Back

As x→∞, f(x)→∞ and as x→-∞, f(x)→∞.

Front

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

Back

The end behavior will be that both ends of the graph fall: as x→∞, y→-∞ and as x→-∞, y→-∞.

Front

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

Back

As x→∞, y→∞ and as x→-∞, y→-∞.

Front

What does it indicate if a graph approaches a horizontal line as x approaches ±∞?

Back

It indicates that the function has a horizontal asymptote.

Front

What is the significance of the leading term in determining end behavior?

Back

The leading term dictates the direction of the graph as x approaches infinity or negative infinity, influencing whether the graph rises or falls.

Front

How can you describe the end behavior of a function using limits?

Back

You can describe it using limits: lim (x→∞) f(x) and lim (x→-∞) f(x) to determine the behavior as x approaches infinity.