New SAT Math - No Calculator

Master essential math concepts and problem-solving skills tested on the New SAT without the use of a calculator.

Linear Equations and InequalitiesExponents and RadicalsRatios, Proportions, and Percents
Quadratic Equations and FactoringFunctions and Their PropertiesSystems of Equations
Budgeting and Personal FinanceMeasurement and Geometry in Everyday LifeTravel and Planning
Smart Estimation and Mental MathTime Management and PacingAnswer Checking and Error Prevention
Linear Equations and...Exponents and Radica...Ratios, Proportions,...Quadratic Equations ...Functions and Their ...Systems of EquationsBudgeting and Person...Measurement and Geom...Travel and PlanningSmart Estimation and...Time Management and ...Answer Checking and ...
Advanced Topics

Functions and Their Properties

Mapping Inputs to Outputs

A function assigns each input exactly one output. Understanding how functions behave is crucial for the SAT.

Function Notation

If \( f(x) = 2x + 3 \), then \( f(4) = 2(4) + 3 = 11 \).

Domain and Range

  • Domain: All possible input values.
  • Range: All possible output values.

Transformations

Shifting, stretching, or reflecting the graph changes the function's behavior.

Real-World Connections

Functions model everything from population growth to temperature changes.

Examples

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

  • A function representing the cost of a taxi ride: \( C(m) = 2 + 1.5m \), where \( m \) is miles.

In a Nutshell

Functions describe unique input-output relationships and model real situations.

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Systems of Equations