CLEP Precalculus

CLEP Precalculus covers essential mathematical concepts and skills necessary for success in calculus and higher-level mathematics.

Functions and Their PropertiesPolynomials and Rational ExpressionsExponential and Logarithmic Functions
Trigonometric Functions and ApplicationsAnalytic GeometrySequences, Series, and Mathematical Induction
Modeling Population GrowthAnalyzing Sound WavesOptimizing Profits with Quadratic Functions
Mastering Calculator SkillsTime Management and Question PrioritizationActive Note-Taking and Formula Memorization
Functions and Their ...Polynomials and Rati...Exponential and Loga...Trigonometric Functi...Analytic GeometrySequences, Series, a...Modeling Population ...Analyzing Sound Wave...Optimizing Profits w...Mastering Calculator...Time Management and ...Active Note-Taking a...
Basic Concepts

Functions and Their Properties

Understanding the Language of Functions

Functions are the backbone of precalculus! A function links each input to exactly one output, acting like a special machine following a set rule. Understanding functions helps you model and solve real-life problems, from predicting profits to analyzing scientific data.

Types of Functions

  • Linear Functions: Graph as straight lines; follow the pattern \( f(x) = mx + b \).
  • Quadratic Functions: Have a squared variable; look like \( f(x) = ax^2 + bx + c \).
  • Exponential and Logarithmic Functions: Involve exponents and their inverses.

Key Properties

  • Domain: All possible inputs.
  • Range: All possible outputs.
  • Intercepts: Where the graph meets the axes.
  • Increasing/Decreasing: Where the function rises or falls.

Visualizing Functions

Graphing helps you see how a function behaves and spot important features like symmetry or turning points.

Why Functions Matter

Functions describe relationships in science, business, and technology. Whether tracking a rocket’s height or modeling population growth, functions are everywhere!

Key Formula

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

Examples

  • The function \( f(x) = 2x + 3 \) gives the output 7 when \( x = 2 \).

  • The quadratic function \( f(x) = x^2 - 4 \) has domain all real numbers and range \( y \geq -4 \).

In a Nutshell

A function assigns each input exactly one output and can be analyzed by its domain, range, and graph.

Key Terms

Function
A rule that assigns to each input exactly one output.
Domain
All possible input values for a function.
Range
All possible output values for a function.
Next
Polynomials and Rational Expressions