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

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

Back

The degree of a polynomial determines the number of times the graph can turn, influencing whether the ends of the graph go up or down.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

How does the sign of the leading coefficient affect end behavior?

Back

If the leading coefficient is positive, the graph will rise to the right; if negative, it will fall to the right.

Front

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

Back

As x → ±∞, f(x) → +∞.

Front

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

Back

As x → ±∞, f(x) → -∞.

Front

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

Back

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

Front

Describe the end behavior of the polynomial f(x) = x^3 - 4x + 1.

Back

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

Front

Describe the end behavior of the polynomial f(x) = -2x^4 + 3x^2 - 1.

Back

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