End Behavior

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

What does an odd degree polynomial indicate about its end behavior?

Back

An odd degree polynomial will have opposite end behaviors; as x → ∞, f(x) → ∞ and as x → -∞, f(x) → -∞.

Front

What does an even degree polynomial indicate about its end behavior?

Back

An even degree polynomial will have the same end behaviors; as x → ∞, f(x) → ∞ and as x → -∞, f(x) → ∞.

Front

What does y → ∞ signify in terms of graph behavior?

Back

y → ∞ signifies that the graph rises without bound as x approaches a certain value.

Front

What does y → -∞ signify in terms of graph behavior?

Back

y → -∞ signifies that the graph falls without bound as x approaches a certain value.

Front

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

Back

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

Front

What is the end behavior of f(x) = x^2 + 3?

Back

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 leading term of the polynomial.

Front

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

Back

The leading term is 5x^4.

Front

What is the significance of the leading coefficient in determining end behavior?

Back

The leading coefficient determines whether the ends of the graph rise or fall; positive leads to rising ends, negative leads to falling ends.