Praxis Math

Praxis Mathematics examination for teacher certification.

Advanced Topics

Functions and Graphs

Exploring Mathematical Relationships

Functions show how one quantity depends on another. Graphs provide a visual way to understand these relationships and spot trends.

What Is a Function?

A function assigns each input exactly one output. It’s like a machine: put something in, get something out.

Graphing Functions

Plotting points on a coordinate plane helps you see patterns, such as lines (linear functions) or curves (quadratic functions).

Interpreting Graphs

Reading graphs helps you analyze data and make predictions—skills essential for teaching and real-world decision-making.

Formula

\( f(x) = mx + b \) is the equation for a straight line, where \( m \) is the slope and \( b \) is the y-intercept.

Key Formula

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

Examples

  • Graphing the line \( y = 2x + 1 \) on a coordinate plane.

  • Interpreting a temperature vs. time graph to find daily trends.

In a Nutshell

Functions and their graphs show how quantities change together.

Key Terms

Function
A rule that assigns each input exactly one output.
Slope
The rate at which a line increases or decreases.