End Behavior

Front

What is end behavior in the context of polynomial functions?

Back

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

Front

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

Back

The end behavior can be determined by the leading term of the polynomial and its degree.

Front

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

Back

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

Front

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

Back

It means that as x decreases without bound, the function values also decrease without bound.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

If a polynomial has an even degree, what can be said about its end behavior?

Back

If the leading coefficient is positive, both ends of the graph will rise; if negative, both ends will fall.

Front

If a polynomial has an odd degree, what can be said about its end behavior?

Back

If the leading coefficient is positive, the left end will fall and the right end will rise; if negative, the left end will rise and the right end will fall.

Front

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

Back

The leading coefficient determines the direction of the graph's ends based on the degree of the polynomial.

Front

Describe the end behavior of the polynomial f(x) = x^4 + 3x^2 - 5.

Back

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

Front

Describe the end behavior of the polynomial f(x) = -2x^3 + x + 1.

Back

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