End Behavior

Front

What is end behavior in the context of graphing functions?

Back

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

Front

How do you denote the end behavior of a function as x approaches positive infinity?

Back

You can denote it as: x → ∞, f(x) → (value), where (value) is the limit of f(x) as x approaches ∞.

Front

What does it mean if a function's end behavior is described as x → ∞, f(x) → ∞?

Back

It means that as x increases without bound, the function f(x) also increases without bound.

Front

What does it indicate if a function's end behavior is x → -∞, f(x) → -∞?

Back

It indicates that as x decreases without bound, the function f(x) also decreases without bound.

Front

If a function has end behavior x → ∞, f(x) → 0, what does this imply?

Back

This implies that as x increases, the function approaches a value of 0.

Front

What is the significance of the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by its leading term and degree, which influences how the graph behaves at the extremes.

Front

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

Back

The end behavior of a rational function can be determined by analyzing the degrees of the numerator and denominator.

Front

What does it mean if a graph approaches a horizontal asymptote as x approaches ±∞?

Back

It means that the function's values are getting closer to a specific constant value as x moves towards positive or negative infinity.

Front

What is the end behavior of the function f(x) = x^2 as x approaches ±∞?

Back

As x → ∞, f(x) → ∞ and as x → -∞, f(x) → ∞.

Front

For the function f(x) = -x^3, what is the end behavior as x approaches ±∞?

Back

As x → ∞, f(x) → -∞ and as x → -∞, f(x) → ∞.