ACT Math Test

The ACT Math Test assesses students' mathematical skills and problem-solving abilities in preparation for college admission.

Numbers and OperationsAlgebraic Expressions and EquationsGeometry and Measurement
Functions and ModelingStatistics and ProbabilityAdvanced Algebra and Systems of Equations
Using Math in Financial DecisionsMath in Science and EngineeringMath in Everyday Problem-Solving
Pacing Yourself During the TestEliminating Wrong AnswersChecking Your Work Efficiently
Numbers and Operatio...Algebraic Expression...Geometry and Measure...Functions and Modeli...Statistics and Proba...Advanced Algebra and...Using Math in Financ...Math in Science and ...Math in Everyday Pro...Pacing Yourself Duri...Eliminating Wrong An...Checking Your Work E...
Advanced Topics

Functions and Modeling

Exploring Functions

Functions are mathematical machines that turn inputs into outputs. On the ACT, you'll identify, interpret, and write function rules, as well as analyze graphs.

What You Need to Know

  • Function Notation: \(f(x)\) means the value of the function at \(x\).
  • Interpreting Graphs: Understand what graphs say about relationships.
  • Linear vs Nonlinear Functions: Spot straight lines vs curves.
  • Modeling Real-Life Situations: Translate scenarios into functions.

Application

Functions help you predict outcomes, like calculating your earnings based on hours worked.

Watch Out

  • Check for domain restrictions (which values are allowed for \(x\)).
  • Understand how changes in the input affect the output.

Key Formula

\[f(x) = mx + b\]

Examples

  • Using \(f(x) = 3x + 2\) to find your weekly pay if you work \(x\) hours.

  • Reading a graph to determine when a car reaches 60 miles per hour.

In a Nutshell

Functions describe how quantities change and help make predictions.

Key Terms

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