SAT Math

Master the essential math concepts and problem-solving skills needed to excel on the SAT.

Algebra FundamentalsWorking with FunctionsData Analysis and Statistics
Quadratic Equations and ParabolasSystems of EquationsAdvanced Geometry and Trigonometry
Budgeting and Personal FinanceSports Stats and PerformanceShopping Smarts
Pacing and Time ManagementSmart Guessing and Elimination
Algebra FundamentalsWorking with Functio...Data Analysis and St...Quadratic Equations ...Systems of EquationsAdvanced Geometry an...Budgeting and Person...Sports Stats and Per...Shopping SmartsPacing and Time Mana...Smart Guessing and E...
Basic Concepts

Working with Functions

Understanding Functions

Functions are like machines: you put something in (the input), the machine does its magic, and you get something out (the output).

A function can be written as \( f(x) \), where \( x \) is the input.

Evaluating Functions

If \( f(x) = 2x + 3 \), and you want to know \( f(4) \):

  1. Substitute 4 for \( x \): \( f(4) = 2(4) + 3 = 8 + 3 = 11 \).

Graphs and Tables

Functions can be shown as graphs or tables. Seeing patterns helps with predictions and understanding trends.

Real-Life Connections

  • Predicting your phone bill based on usage.
  • Figuring out how many points you need on a test to reach your target grade.

Common Function Types

  • Linear: \( f(x) = mx + b \)
  • Quadratic: \( f(x) = ax^2 + bx + c \)
  • Exponential: \( f(x) = a \cdot b^x \ )

Examples

  • If \( f(x) = x^2 \), then \( f(5) = 25 \).

  • A taxi fare: \( f(miles) = 2.50 + 1.75 \times miles \).

In a Nutshell

Functions connect inputs to outputs, showing how one thing depends on another.

Key Terms

Function
A rule that assigns exactly one output to each input.
Linear
A function whose graph is a straight line.
Next
Data Analysis and Statistics