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.

$f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$

$f(x) = \frac{p(x)}{q(x)}$, where $p(x)$ and $q(x)$ are polynomials.

$\frac{f(b) - f(a)}{b - a}$

$m = \frac{y_2 - y_1}{x_2 - x_1}$

If $f(x) = \frac{ax^n + ...}{bx^n + ...}$, then $y = \frac{a}{b}$

$y = 0$

There is no horizontal asymptote. Consider long division to find slant asymptote if the degree of the numerator is exactly one more than the degree of the denominator.

Set $f(x) = 0$ and solve for $x$.

Set the denominator $q(x) = 0$ and solve for $x$, excluding any values that are also zeros of the numerator.

Find common factors in the numerator and denominator. The $x$-value where the factor equals zero is the location of the hole.

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.