End Behavior of Polynomials

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 does it mean when x → -∞?

Back

It means that x is approaching negative infinity, or moving towards the left on the number line.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean when x → ∞?

Back

It means that x is approaching positive infinity, or moving towards the right on the number line.

Tags

CCSS.HSF-IF.C.7A

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, specifically its degree and leading coefficient.

Front

What is the leading term of the polynomial f(x) = -7x^3 + 2x - 1?

Back

The leading term is -7x^3.

Front

If the leading coefficient is negative and the degree is odd, what is the end behavior?

Back

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

Front

If the leading coefficient is positive and the degree is even, what is the end behavior?

Back

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

Front

What is the end behavior of the function f(x) = x^4 + 3x^3 - 4x + 1?

Back

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

Front

What is the end behavior of the function f(x) = -2x^7 + 2x^4 + 4?

Back

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

Front

What does the term 'end behavior' refer to in polynomial functions?

Back

End behavior refers to the values of f(x) as x approaches positive or negative infinity.