ACT Math

A comprehensive course covering the essential math concepts and strategies needed to excel on the ACT.

Numbers, Operations, and Number PropertiesAlgebraic Expressions and EquationsGeometry Fundamentals
Functions and GraphsSystems of Equations and InequalitiesProbability, Statistics, and Data Interpretation
Math in Everyday LifeCareers That Use MathMath in Sports and Games
Time Management and PacingPlugging In and Answer Choice StrategiesReading and Translating Word Problems
Numbers, Operations,...Algebraic Expression...Geometry Fundamental...Functions and GraphsSystems of Equations...Probability, Statist...Math in Everyday Lif...Careers That Use Mat...Math in Sports and G...Time Management and ...Plugging In and Answ...Reading and Translat...
Advanced Topics

Functions and Graphs

Understanding Functions

Functions are mathematical machines: you put in a number (input), and you get a number out (output).

Function Notation

  • Written as \( f(x) \), where \( x \) is the input
  • Example: If \( f(x) = 2x + 1 \), then \( f(3) = 7 \)

Graphing Functions

  • The x-axis (horizontal) represents inputs
  • The y-axis (vertical) represents outputs
  • The shape of the graph tells you about the relationship

ACT Connections

You may be asked to interpret graphs or match equations to their graphs.

Real-Life Functions

Functions model things like cost over time, population growth, or speed.

Tips

  • Find patterns in tables or graphs
  • Use substitution to check your answers

Key Formula

\[f(x) = ax^2 + bx + c\]

Examples

  • If \( f(x) = x^2 - 2x \), then \( f(4) = 16 - 8 = 8 \)

  • A line with equation \( y = 3x - 2 \) has a slope of 3 and crosses the y-axis at -2.

In a Nutshell

Functions link inputs and outputs, and their graphs reveal relationships.

Key Terms

Function
A rule that assigns exactly one output to each input.
Slope
The steepness of a line, calculated as rise over run.
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Systems of Equations and Inequalities