Describes the function's output values as input values approach positive or negative infinity.

The term with the highest degree in a polynomial function.

The coefficient of the term with the highest degree.

As x approaches infinity, the function f(x) also approaches infinity.

As x approaches negative infinity, the function f(x) also approaches negative infinity.

The highest power of the variable in the polynomial; influences the shape and end behavior.

Determines whether the function increases or decreases without bound as x approaches infinity or negative infinity.

The function's values become infinitely large (positive infinity).

The function's values become infinitely small (negative infinity).

A function that can be expressed in the form $f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0$, where n is a non-negative integer.

Identify the leading term: $5x^3$. Since the coefficient is positive and the degree is odd, as $x \to \infty$, $f(x) \to \infty$ and as $x \to -\infty$, $f(x) \to -\infty$.

Identify the leading term: $-3x^4$. Since the coefficient is negative and the degree is even, as $x \to \pm \infty$, $g(x) \to -\infty$.

1. Identify the leading term. 2. Note the sign of the leading coefficient. 3. Note the degree of the leading term. 4. Apply the rules for even/odd degree and positive/negative coefficient.

Expand to find the leading term: $2x^3$. Positive coefficient, odd degree. As $x \to \infty$, $f(x) \to \infty$; as $x \to -\infty$, $f(x) \to -\infty$.

Expand to find the leading term: $-x^6$. Negative coefficient, even degree. As $x \to \pm \infty$, $f(x) \to -\infty$.

Leading term is $7x^5$. Positive coefficient, odd degree. As $x \to \infty$, $f(x) \to \infty$; as $x \to -\infty$, $f(x) \to -\infty$.

Leading term is $-x^6$. Negative coefficient, even degree. As $x \to \pm \infty$, $f(x) \to -\infty$.

Leading term is $-2x^3$. Negative coefficient, odd degree. As $x \to \infty$, $f(x) \to -\infty$; as $x \to -\infty$, $f(x) \to \infty$.

Leading term is $4x^4$. Positive coefficient, even degree. As $x \to \pm \infty$, $f(x) \to \infty$.

Expand to find the leading term: $x^3$. Positive coefficient, odd degree. As $x \to \infty$, $f(x) \to \infty$; as $x \to -\infty$, $f(x) \to -\infty$.

For large absolute values of x, the leading term dominates the polynomial's value, dictating its end behavior.

As $x$ approaches $\pm \infty$, $f(x)$ approaches $\infty$.

As $x$ approaches $\pm \infty$, $f(x)$ approaches $-\infty$.

As $x$ approaches $\infty$, $f(x)$ approaches $\infty$, and as $x$ approaches $-\infty$, $f(x)$ approaches $-\infty$.

As $x$ approaches $\infty$, $f(x)$ approaches $-\infty$, and as $x$ approaches $-\infty$, $f(x)$ approaches $\infty$.

As x approaches infinity, the leading term's contribution to the function's value becomes overwhelmingly larger than all other terms.

Even degree polynomials have the same end behavior as x approaches both positive and negative infinity.

Odd degree polynomials have opposite end behaviors as x approaches positive and negative infinity.

End behavior describes the limits of the function as x approaches positive or negative infinity.

It provides a general understanding of how the function behaves for very large or very small values of x and is foundational for further analysis.