Free tutorials on graphing functions, with examples, detailed solutions and matched problems. The properties of the graphs of linear, quadratic, rational, trigonometric, absolute value, logarithmic, exponential and piecewise functions are analyzed in details. Graphing polar equations are also included. Detailed solutions and explanations to the examples are included. Concepts such as asymptotes for graphs of rational, logarithmic and exponential functions are explored numerically.

Graphing Polar Equations. This is tutorial on graphing polar equations by hand, or sketching, to help you gain deep understanding of these equations. Several examples with detailed solutions are presented.

Graph Piecewise Functions. Many examples of piecewise functions and several examples on how to graph these functions with detailed solutions.

Graphing Linear Functions. A step by step tutorial with examples and detailed solutions to graph linear functions.

Graphing Square Root Functions. A step by step tutorial on graphing and sketching square root functions. The graph, domain, range of these functions and other properties are discussed.

Graphing Quadratic Functions. A step by step tutorial on how to determine the properties of the graph of quadratic functions and graph them. Properties, of these functions, such as domain, range, x and y intercepts, minimum and maximum are thoroughly discussed.

Graph of Rational Functions  Sketching. How to graph a rational function? A step by step tutorial. The properties such as domain, vertical and horizontal asymptotes of a rational function are also investigated.

Graph of Sine, a * sin(b x + c), Function. Graphing and sketching sine functions of the form f (x) = a * sin (b x + c); step by step tutorial.

Graphing arcsin(x) functions. Graphing and sketching arcsin functions where also the domain and range of these functions and other properties are discussed.

Graphing Tangent Functions. A step by step tutorial on graphing and sketching tangent functions. The graph, domain, range and vertical asymptotes of these functions and other properties are examined.

Graphs of Logarithmic Functions. Graphing and sketching logarithmic functions: a step by step tutorial. The properties such as domain, range, vertical asymptotes and intercepts of the graphs of these functions are also examined in details.

Graphs of Exponential Functions. Graphing and sketching exponential functions: step by step tutorial. The properties such as domain, range, horizontal asymptotes and intercepts of the graphs of these functions are also examined in details.

Graph, Domain and Range of Absolute Value Functions. This is a step by step tutorial on how to graph functions with absolute value. Properties of the graph of these functions such as domain, range, x and y intercepts are also discussed.

Free graph paper is available.

