Functions in Algebra

A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range)
Notation: f(x) = output value
Domain: set of all input values (x) for which the function is defined
Range: set of all possible output values (y)
Key concepts:
- Function notation: f(x) = 2x + 1
- Domain and range: identify the domain and range of a function
- Evaluating functions: find the output value for a given input value
- Composition of functions: combine two or more functions
- Inverse functions: find the input value for a given output value

A system of equations is a set of two or more equations that must be true at the same time
Types of systems:
- Independent systems: have a unique solution
- Dependent systems: have infinitely many solutions
- Inconsistent systems: have no solution
Methods for solving systems:
- Substitution method: substitute one equation into the other
- Elimination method: add or subtract equations to eliminate one variable
- Graphing method: graph the equations on the same coordinate plane

An inequality is a statement that one expression is greater than, less than, or equal to another expression
Notation: >, <, ≥, ≤, ≠
Key concepts:
- Solving linear inequalities: solve for x
- Graphing linear inequalities: graph the solution on a number line
- Compound inequalities: solve and graph systems of inequalities

A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication
Types of polynomials:
- Monomials: single term polynomials
- Binomials: two-term polynomials
- Trinomials: three-term polynomials
Key concepts:
- Adding and subtracting polynomials: combine like terms
- Multiplying polynomials: use the distributive property
- Factoring polynomials: express a polynomial as a product of simpler polynomials
- Solving polynomial equations: solve for x

A function is a relation between a set of inputs (domain) and a set of possible outputs (range), where each input value corresponds to exactly one output value.
Function notation is f(x) = output value, where x is the input value and f(x) is the output value.
The domain is the set of all input values (x) for which the function is defined, while the range is the set of all possible output values (y).
Evaluating functions involves finding the output value for a given input value, using the function notation.
Composition of functions involves combining two or more functions, whereas inverse functions involve finding the input value for a given output value.

A system of equations is a set of two or more equations that must be true at the same time, and can be classified as independent (unique solution), dependent (infinitely many solutions), or inconsistent (no solution).
The substitution method involves substituting one equation into the other, while the elimination method involves adding or subtracting equations to eliminate one variable.
The graphing method involves graphing the equations on the same coordinate plane to find the solution.

Graphing is a visual representation of a function or equation, where the x-axis represents the input values (x) and the y-axis represents the output values (y).
The origin is the point where the x-axis and y-axis intersect, at (0, 0), and the quadrants are the four regions of the coordinate plane.
Graphing functions and equations involves identifying the graph of a function or equation, while intercepts involve finding the x-intercepts and y-intercepts of a graph.

An inequality is a statement that one expression is greater than, less than, or equal to another expression, and can be notated as >, <, ≥, or ≤.

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