CLEP College Algebra

CLEP College Algebra covers fundamental algebraic concepts and skills necessary for success in college-level mathematics courses.

Basic Concepts

Functions and Their Graphs

What is a Function?

A function is a rule that assigns exactly one output to each input. It's like a math vending machine: put a number in, get a unique number out.

Function Notation

Functions are written as \( f(x) \), where \( x \) is the input. For example, \( f(x) = 2x + 1 \).

Graphing Functions

The graph of a function is a picture of all the input-output pairs. Linear functions graph as straight lines, while quadratic functions form parabolas.

  • Intercepts: Where the graph crosses the axes.
  • Slope: The steepness of a straight line.

Real-World Use

Functions model everything from calculating your phone bill to predicting how fast a plant grows.

Examples

  • Graph \( f(x) = 3x \) by plotting points for \( x = -1, 0, 1 \).

  • If \( f(x) = x^2 \), then \( f(3) = 9 \).

In a Nutshell

Functions pair each input with only one output, and their graphs help us visualize relationships.