End Behavior & Zeros of Polynomials

Front

What is the term that affects the end behavior of a polynomial?

Back

Leading Term

Front

What is the factored form of the function f(x) = x³ + 7x² - 2x - 14?

Back

f(x) = (x² - 2)(x + 7)

Front

Determine the end behavior of the graph of f(x) = -7x³ + 2x - 1.

Back

As x → ∞, f(x) → -∞; As x → -∞, f(x) → ∞.

Front

Determine the end behavior of the graph of f(x) = 3x⁴ + 2x - 5.

Back

As x → ∞, f(x) → ∞; As x → -∞, f(x) → ∞.

Front

What does it mean if a zero of a polynomial crosses the x-axis?

Back

The polynomial changes sign at that zero.

Front

What does it mean if a zero of a polynomial bounces at the x-axis?

Back

The polynomial does not change sign at that zero.

Front

What does it mean if a zero of a polynomial turns at the x-axis?

Back

The polynomial has a multiplicity greater than 2 at that zero.

Front

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

Back

Look at the leading term's degree and coefficient.

Front

What is the end behavior of a polynomial with an even degree and a positive leading coefficient?

Back

As x → ∞, f(x) → ∞; As x → -∞, f(x) → ∞.

Front

What is the end behavior of a polynomial with an odd degree and a negative leading coefficient?

Back

As x → ∞, f(x) → -∞; As x → -∞, f(x) → ∞.