Define the end behavior as $$x \rightarrow -\infty$$ for a function that approaches negative infinity.

As $$x \rightarrow -\infty, f(x) \rightarrow -\infty$$ .

Define the end behavior as $$x \rightarrow \infty$$ for a function that approaches positive infinity.

As $$x \rightarrow \infty, f(x) \rightarrow \infty$$ .

What does it mean if a function approaches negative infinity as $$x \rightarrow \infty$$ ?

It means that as the input values increase without bound, the output values decrease without bound, represented as $$x \rightarrow \infty, f(x) \rightarrow -\infty$$ .

What does it mean if a function approaches positive infinity as $$x \rightarrow -\infty$$ ?

It means that as the input values decrease without bound, the output values increase without bound, represented as $$x \rightarrow -\infty, f(x) \rightarrow \infty$$ .

What is the end behavior of the function $$f(x) = x^3$$ ?

As $$x \rightarrow -\infty, f(x) \rightarrow -\infty$$ and as $$x \rightarrow \infty, f(x) \rightarrow \infty$$ .

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

As $$x \rightarrow -\infty, f(x) \rightarrow -\infty$$ and as $$x \rightarrow \infty, f(x) \rightarrow -\infty$$ .

What is the end behavior of the function $$f(x) = \frac{1}{x}$$ ?

As $$x \rightarrow -\infty, f(x) \rightarrow 0$$ and as $$x \rightarrow \infty, f(x) \rightarrow 0$$ .

What is the end behavior of the function $$f(x) = e^{-x}$$ ?

As $$x \rightarrow -\infty, f(x) \rightarrow \infty$$ and as $$x \rightarrow \infty, f(x) \rightarrow 0$$ .

What is the end behavior of the function $$f(x) = \sin(x)$$ ?

The end behavior of $$f(x) = \sin(x)$$ does not approach a limit as $$x \rightarrow \infty$$ or $$x \rightarrow -\infty$$ ; it oscillates between -1 and 1.

How does the degree of a polynomial affect its end behavior?

The degree of a polynomial determines the direction of the end behavior: even degrees lead to the same end behavior (both up or both down), while odd degrees lead to opposite end behaviors.

What is the end behavior of a rational function $$f(x) = \frac{x^2 - 1}{x^2 + 1}$$ ?

As $$x \rightarrow -\infty, f(x) \rightarrow 1$$ and as $$x \rightarrow \infty, f(x) \rightarrow 1$$ .

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

As $$x \rightarrow -\infty, f(x) \rightarrow \infty$$ and as $$x \rightarrow \infty, f(x) \rightarrow \infty$$ .

End Behavior Flashcards

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What is end behavior in mathematics?

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

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