Sect. 5.2 End Behavior of Polynomial Function Practice

Front

What is the leading term of a polynomial function?

Back

The leading term is the term in a polynomial that has the highest degree, which determines the end behavior of the function.

Front

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

Back

The degree of a polynomial indicates the highest power of x. Even-degree polynomials have the same end behavior on both sides, while odd-degree polynomials have opposite end behaviors.

Front

What is the end behavior of a polynomial function as x approaches positive infinity?

Back

The end behavior as x approaches positive infinity depends on the leading term's coefficient and degree.

Front

What is the end behavior of a polynomial function as x approaches negative infinity?

Back

The end behavior as x approaches negative infinity also depends on the leading term's coefficient and degree.

Front

For the polynomial f(x) = -7x^3 + 2x - 1, what is the end behavior as x approaches infinity?

Back

As x → ∞, f(x) → -∞.

Front

For the polynomial f(x) = 3x^4 + 2x - 5, what is the end behavior as x approaches negative infinity?

Back

As x → -∞, f(x) → ∞.

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 as x approaches positive or negative infinity.

Front

What is the end behavior of the polynomial function f(x) = 6x^4 + 3x^3 - 2x + 14?

Back

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

Front

What is the general form of a polynomial function?

Back

A polynomial function is expressed as f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0, where a_n ≠ 0.

Front

How can you determine the end behavior of a polynomial function from its graph?

Back

You can observe the direction in which the graph heads as x approaches positive and negative infinity.