Polynomial End Behavior Review

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity.

Front

What determines the end behavior of a polynomial function?

Back

The end behavior is determined by the leading term of the polynomial, specifically its degree and leading coefficient.

Front

What is the leading term of the polynomial f(x) = 4x^5 - 3x^3 + 2?

Back

The leading term is 4x^5.

Front

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

Back

If the degree is even, both ends of the graph will either rise or fall together. If the degree is odd, one end will rise while the other falls.

Front

What is the end behavior of f(x) = x^4 as x → ∞ and x → -∞?

Back

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

Front

What is the end behavior of f(x) = -x^3 as x → ∞ and x → -∞?

Back

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

Front

Define a polynomial's x-intercept.

Back

An x-intercept is a point where the graph of the polynomial crosses the x-axis, meaning f(x) = 0.

Front

What is the relationship between roots and x-intercepts?

Back

Roots and x-intercepts are the same; they both refer to the values of x for which the polynomial equals zero.

Front

What is the end behavior of f(x) = 2x^2 + 3 as x → ∞ and x → -∞?

Back

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

Front

What is the end behavior of f(x) = -2x^2 + 5 as x → ∞ and x → -∞?

Back

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