4.1 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 if a polynomial has an even degree and a positive leading coefficient?

Back

If a polynomial has an even degree and a positive leading coefficient, the end behavior will be: as x → -∞, f(x) → +∞ and as x → +∞, f(x) → +∞.

Front

What does it mean if a polynomial has an odd degree and a negative leading coefficient?

Back

If a polynomial has an odd degree and a negative leading coefficient, the end behavior will be: as x → -∞, f(x) → +∞ and as x → +∞, f(x) → -∞.

Front

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

Back

The end behavior can be determined by the degree of the polynomial and the sign of the leading coefficient.

Front

What is the leading coefficient of the polynomial f(x) = 2x^3 - 5x + 1?

Back

The leading coefficient is 2.

Front

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

Back

The degree of the polynomial is 5.

Front

If a polynomial function has a degree of 4, what can you say about its end behavior?

Back

If the leading coefficient is positive, as x → ±∞, f(x) → +∞. If the leading coefficient is negative, as x → ±∞, f(x) → -∞.

Front

What is the end behavior of the polynomial f(x) = x^4 - 2x^2 + 1?

Back

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

Front

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

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.