End behavior describes what happens to the function's values as $x$ approaches positive or negative infinity. It's determined by the leading term (degree and leading coefficient).

The degree determines the maximum number of turning points and the end behavior. Even degree: ends go in the same direction. Odd degree: ends go in opposite directions.

The sign of the leading coefficient determines whether the graph rises or falls as $x$ approaches positive or negative infinity. Positive: rises to the right. Negative: falls to the right.

If $x = a$ is a zero of a polynomial, then $(x - a)$ is a factor of the polynomial.

Vertical asymptotes occur where the denominator of a rational function equals zero and the numerator does not. They indicate values of $x$ where the function approaches infinity.

Horizontal asymptotes describe the behavior of the function as $x$ approaches positive or negative infinity. They are determined by comparing the degrees of the numerator and denominator.

Holes occur when a factor cancels out in both the numerator and denominator. The function is undefined at that $x$-value, but the limit exists.

Compare the degrees of the numerator and denominator. If the degree of the denominator is greater, $y=0$. If the degrees are equal, $y$ is the ratio of leading coefficients.

The rate of change (slope) is constant for linear functions, meaning the function increases or decreases at a steady rate.

The rate of change varies for quadratic functions, meaning the function's increase or decrease is not constant.

A value of $x$ where the function approaches infinity or negative infinity, and the function is undefined.

A value of $x$ where the function is undefined, but the limit exists. It occurs due to a common factor in the numerator and denominator.

Observe the behavior of the graph as $x$ approaches positive and negative infinity. Note whether the graph rises or falls on each end.

The zeros are the $x$-intercepts of the graph, where the graph crosses or touches the $x$-axis.

It's a straight line, and the slope of the line represents the constant rate of change.

It's a parabola, and the rate of change varies, increasing or decreasing depending on the location on the parabola.

It appears as an open circle (or removable discontinuity) at a specific point on the graph.

If the multiplicity is odd, the graph crosses the x-axis. If the multiplicity is even, the graph touches the x-axis and turns around.

It shows the value that the function approaches as x goes to infinity or negative infinity.

If the graph rises to the right, the leading coefficient is positive. If the graph falls to the right, the leading coefficient is negative.

A sum of terms, each consisting of a coefficient and a variable raised to a non-negative integer power.

The highest power of the variable in the polynomial.

A ratio of two polynomial functions, expressed as $f(x) = p(x)/q(x)$.

A vertical line $x = a$ where the function approaches infinity or negative infinity as $x$ approaches $a$.

A horizontal line $y = b$ that the function approaches as $x$ approaches infinity or negative infinity.

A point where the function is undefined because a factor cancels out in both the numerator and denominator.

How quickly a function's output changes with respect to its input.

Zeros of a polynomial function that are complex numbers.

The coefficient of the term with the highest power in a polynomial.

The behavior of a function as $x$ approaches positive or negative infinity.