ACT Math

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

Numbers and OperationsAlgebraic Expressions and EquationsGeometry Basics
Functions and GraphsProbability and StatisticsQuadratic Equations and Polynomials
Math in Personal FinanceGeometry in Real LifeStatistics in Everyday Decisions
Time Management on the ACTPlug-In and Backsolving
Numbers and Operatio...Algebraic Expression...Geometry BasicsFunctions and GraphsProbability and Stat...Quadratic Equations ...Math in Personal Fin...Geometry in Real Lif...Statistics in Everyd...Time Management on t...Plug-In and Backsolv...
Advanced Topics

Functions and Graphs

Mapping Inputs to Outputs

A function is a rule that assigns each input exactly one output. Functions appear on the ACT as equations, tables, and graphs.

Reading Graphs

  • The \( x \)-axis is horizontal; the \( y \)-axis is vertical.
  • The graph of \( y = mx + b \) is a straight line.

Domain and Range

  • Domain: All possible \( x \) values.
  • Range: All possible \( y \) values.

Real-World Application

Use functions to track things like speed, costs, or population growth over time.

Key Skill

Interpreting function notation, like \( f(x) \), and evaluating for specific values.

Example Formula

  • Slope of a line: \( m = \frac{y_2 - y_1}{x_2 - x_1} \)

Key Formula

\[m = \frac{y_2 - y_1}{x_2 - x_1}\]

Examples

  • If \( f(x) = 2x + 1 \), then \( f(3) = 7 \)

  • The graph of \( y = x^2 \) is a parabola

In a Nutshell

Functions describe relationships, and graphs help you see them visually.

Key Terms

Function
A relationship that assigns exactly one output to each input.
Domain
All possible input values for a function.
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Probability and Statistics