Linear: Straight line, constant rate of change | Polynomial: Curve, changing rate of change

Polynomial: Can be written as a sum of terms with non-negative integer exponents. | Rational: Written as a ratio of two polynomials, may have asymptotes.

Shifts: Translate the graph without changing its shape. | Stretches: Change the shape by compressing or expanding the graph.

Direct: As one quantity increases, the other increases. | Inverse: As one quantity increases, the other decreases.

Domain: Set of possible input values (x). | Range: Set of possible output values (y).

Continuous: A single function defined over its entire domain without any breaks. | Piecewise: Defined by different functions over different intervals of its domain.

Vertical Stretch: Multiplies the y-values by a factor, making the graph taller. | Horizontal Compression: Divides the x-values by a factor, making the graph narrower.

Vertical Shift: Moves the graph up or down by adding or subtracting a constant. | Horizontal Shift: Moves the graph left or right by adding or subtracting a constant from the x-value.

Linear Regression: Finds the best-fitting straight line for the data. | Polynomial Regression: Finds the best-fitting polynomial curve for the data.

Assumptions: Simplifications made about the real-world scenario to create a tractable model. | Restrictions: Constraints on the domain or range of the function based on the real-world context.

A mathematical representation of a real-world situation using a function.

A function defined by multiple sub-functions, each applying to a certain interval of the main function's domain.

A function that can be defined as a quotient of two polynomial functions, i.e., $f(x) = \frac{p(x)}{q(x)}$, where p(x) and q(x) are polynomials.

A relationship where one quantity decreases as another increases, often modeled by a rational function.

The set of all possible input values (x-values) for which the function is defined and makes sense in the real-world context.

The set of all possible output values (y-values) that the function can produce, considering the real-world context.

The simplest form of a function family, used as a basis for transformations. Examples: $y = x^2$, $y = x^3$, $y = \sqrt{x}$.

A change made to a parent function to fit a given data set, including shifts, stretches, compressions, and reflections.

A statistical method used to find the best-fitting linear relationship between two variables in a data set.

A measure of how one quantity changes with respect to another, often representing the slope of a function or its derivative.

It indicates a value where the function is undefined, often due to division by zero. The function approaches infinity (or negative infinity) as x approaches that value.

The graph will consist of different function segments connected or disconnected at specific points, each corresponding to a different interval.

The graph stretches away from the origin. Larger $k$ values mean that for the same $x$, $y$ is larger, and vice versa.

It indicates the value that the function approaches as x goes to positive or negative infinity. This represents a limit on the output of the function.

Look for shifts (left/right, up/down), stretches/compressions (narrower/wider, taller/shorter), and reflections (across x or y axis) compared to the parent function's graph.

It indicates a point where the function is not continuous, which can be a hole, a jump, or a vertical asymptote.

The slope represents the rate of change of the function. A positive slope indicates an increasing function, a negative slope indicates a decreasing function, and a zero slope indicates a constant function.

The domain is the set of all x-values covered by the graph, and the range is the set of all y-values covered by the graph.

It tells you what happens to the function's values as x approaches positive or negative infinity. This is determined by the leading term of the polynomial.

Check if the function is continuous at the boundary points. If there's a jump or a break, the function is discontinuous at that point.