Functions Hub: Tutorials, Graphs, Properties & Applications

Learn the fundamental definitions of mathematical relations, mappings, and ordered pairs.

Master the concept of mathematical functions, the vertical line test, and representation methods.

Learn to identify dependent/independent variables and find the domain and range directly from an equation.

A quick-reference guide detailing the parent graphs and attributes of the most common mathematical functions.

How to algebraically add, subtract, multiply, and divide different functions.

Learn algebraic and graphical techniques to locate the x-intercepts (roots) of various equations.

Understand symmetry across the y-axis and the origin, and how to prove a function is even or odd algebraically.

Analyze functions that repeat their values at regular intervals over their domain.

Analyze slopes, y-intercepts, and graphing techniques for lines in the form f(x) = mx + b.

Detailed tutorial on analyzing and graphing parabolas written in the standard form f(x) = ax² + bx + c.

How to find the vertex, axis of symmetry, and graph parabolas using the form f(x) = a(x-h)² + k.

Understand the geometric and algebraic relationship of multiplying two lines to form a parabola.

Explore the properties and graphs of V-shaped absolute value functions.

Graphing and analyzing the domain, range, and transformations of square root functions.

Properties, end behavior, and graphing techniques for cube root equations.

Explore the graphs and properties of cubic polynomial functions mapping real numbers to their cubes.

Step functions mapping a real number to the least integer greater than or equal to x.

Step functions mapping a real number to the greatest integer less than or equal to x.

Properties and mathematical formulas of the bell-shaped Gaussian curve.

Understand capacity limits, population growth models, and the shape of logistic curves.

Practical real-world word problems translated, modeled, and solved using mathematical functions.