How to Graph a Piecewise Function Online
Learn how to graph piecewise functions with interval restrictions, open and closed endpoints, and continuity checks.
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How to Graph Parametric Equations Online
Graph parametric curves by entering x(t), y(t), choosing a parameter interval, and checking direction and scale.
Read article →How to Graph Polar Equations and Rose Curves
Learn polar coordinates, graph r as a function of angle, and predict the petals and symmetry of rose curves.
Read article →How to Graph Circles, Ellipses, and Implicit Equations
Graph conic sections and relations that are not single-valued functions by using implicit equation mode.
Read article →How to Graph an Inverse Function and Reflect Across y = x
Find inverse functions, graph a function with its inverse, and use reflection across y = x to verify the result.
Read article →How to Identify Holes, Jumps, and Infinite Discontinuities
Distinguish removable, jump, and infinite discontinuities by using limits, function values, and graph behavior.
Read article →How to Find Tangent and Normal Lines to a Curve
Use derivatives to find tangent and normal line equations, then verify both lines on the graph.
Read article →How to Find Concavity and Inflection Points
Use the second derivative to determine concavity, find inflection points, and verify curve shape on a graph.
Read article →How to Analyze a Rational Function Completely
Complete a rational-function analysis: domain, intercepts, holes, asymptotes, extrema, monotonicity, and concavity.
Read article →How to Find the Area Between Two Curves
Find intersection points, identify the upper and lower curves, set up the integral, and verify the bounded region visually.
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