College Algebra

College Algebra covers fundamental algebraic concepts, including functions, equations, and inequalities, essential for higher-level mathematics.

Algebraic Expressions and OperationsSolving Equations and InequalitiesFunctions and Their Properties
Quadratic Equations and ApplicationsExponential and Logarithmic FunctionsSystems of Equations
Budgeting and Personal FinanceScience and Engineering ModelsBusiness and Economics
Practice and Review RegularlyBreak Down Complex Problems
Algebraic Expression...Solving Equations an...Functions and Their ...Quadratic Equations ...Exponential and Loga...Systems of EquationsBudgeting and Person...Science and Engineer...Business and Economi...Practice and Review ...Break Down Complex P...
Basic Concepts

Functions and Their Properties

What is a Function?

A function is a rule that assigns each input exactly one output. Think of it as a vending machine: you select an input (button), it gives you one output (snack).

Function Notation

Written as \(f(x)\), where \(x\) is the input. For example, \(f(x) = 2x + 1\).

Types of Functions

  • Linear: Straight-line graphs (\(f(x) = mx + b\))
  • Quadratic: Parabolas (\(f(x) = ax^2 + bx + c\))
  • Absolute Value: V-shaped (\(f(x) = |x|\))

Key Properties

  • Domain: Possible input values
  • Range: Possible output values
  • Intercepts: Where the graph crosses axes

Why Functions Matter

Functions model real-world relationships—like speed, growth, and finance.

Examples

  • If \(f(x) = 3x - 2\), then \(f(4) = 10\).

  • The function \(g(x) = x^2\) has a domain of all real numbers and a range of all non-negative numbers.

In a Nutshell

A function links each input to exactly one output, and helps model real-world situations.

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Quadratic Equations and Applications