End Behavior

Front

What is end behavior in graphing 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 graph approaches +∞ as x → +∞?

Back

It means that as x increases without bound, the function values (y) also increase without bound.

Front

What does it mean if a graph approaches -∞ as x → -∞?

Back

It means that as x decreases without bound, the function values (y) decrease without bound.

Front

If a graph has end behavior of x → ∞, y → ∞ and x → -∞, y → ∞, what does this indicate?

Back

This indicates that the graph rises to infinity on both ends.

Front

What is the significance of the leading coefficient in polynomial functions regarding end behavior?

Back

The leading coefficient determines the direction of the graph's end behavior: positive leading coefficients lead to upward behavior, while negative coefficients lead to downward behavior.

Front

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

Back

You can determine it by looking at the degree and leading coefficient of the polynomial.

Front

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

Back

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

Front

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

Back

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

Front

What does it mean if a graph approaches y = 0 as x → ±∞?

Back

It indicates that the function is approaching a horizontal asymptote at y = 0.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches ±∞.