Mathematics: Relations and Functions

Relations: A set of ordered pairs defining how inputs relate to outputs.
Functions: A specific type of relation where each input has a single output.
Function Notation: A way to represent functions, typically written as f(x).
Domain: The set of all possible input values (x values) for a function.
Range: The set of all possible output values (y values) for a function.

Parent Functions: The simplest form of functions in a family (e.g., linear, quadratic).
Dependent Variable: The output of a function, which relies on the input or independent variable.
Linear Function: Preserves a constant rate of change; represented as y = mx + b, where m is slope and b is y-intercept.
Quadratic Function: Characterized by the x² term; often in the form y = ax² + bx + c.

Slope-Intercept Form: y = mx + b; describes the relationship in linear equations.
Commutative Property: States that changing the order of numbers does not affect the sum or product (e.g., a + b = b + a).
Associative Property: Indicates that the way numbers are grouped does not change their sum or product (e.g., (a + b) + c = a + (b + c)).
Distributive Property: Describes how to distribute multiplication over addition or subtraction (e.g., a(b + c) = ab + ac).

Bivariate Data: Involves two variables being measured simultaneously.
Box and Whisker Plot: A graphical representation of data that shows the distribution based on five-number summary (min, Q1, median, Q3, max).
Cumulative Frequency Table: Displays total occurrences of data points as they accumulate across intervals.
Measures of Central Tendency: Common measures include mean (average), median (middle value), and mode (most frequent value).

Scatter Plot: A graph used to show relationships between two variables without connecting the dots.
Line of Best Fit: A line that approximates the relationship between two variables, reducing scatter while maintaining the trend.
Parabola: The U-shape graph produced by quadratic functions.

Polynomial: A mathematical expression consisting of variables, coefficients, and positive whole number exponents (e.g., 2x² + 3x + 1).
Monomial: A polynomial with a single term.
Binomial: A polynomial with two terms (e.g., x + 4).
Trinomial: A polynomial with three terms.

Arithmetic Sequence: A sequence with a constant additive rate of change.
Geometric Sequence: A sequence where each term is multiplied by a constant rate of change.

Roots of an Equation: Solutions where the function equals zero, found by identifying x-intercepts on a graph or using factoring techniques.
Solution Set: A collection of values that satisfy an equation or inequality.

Exponent: Indicates how many times to multiply the base by itself.
Coefficient: The numerical factor before a variable in a term.
Zeros of a Graph: Points on the x-axis where the value of the function is zero (intercepts).
Residual: The difference between actual and predicted values, indicating the accuracy of a model.

Correlation: Indicates the strength of the relationship between two variables.
Exponential Functions: Functions representing growth or decay where a constant base is raised to a variable exponent.
Irrational Numbers: Numbers that cannot be expressed as fractions (e.g., √2, π).
Rational Numbers: Numbers that can be expressed as fractions.

Vertical and Horizontal Shifts: Changes to the position of a graph based on function transformations.
Dilation: Alteration of a graph's visual presentation, affecting its width or height.