Look for the leftmost and rightmost points of the graph. If the graph extends indefinitely to the left or right, the domain includes negative or positive infinity, respectively. Note any breaks or ...

All quadratic functions have the same type of curved graphs with a line of symmetry. The graph of the quadratic function \(y = ax^2 + bx + c \) has a minimum turning point when \(a \textgreater 0 \) ...

At its core, continuity implies that small changes in the input of a function result in small changes in its output. More ...

Functions of two variables can be visualized in many ways: heat maps in 2D, contour curves in 2D, wireframes in 3D, surfaces in 3D. We begin by defining a function of two variables, building an array ...

The graph below has a turning point (3, -2). Write down the nature of the turning point and the equation of the axis of symmetry. For the parabola \(y=(x+6)(x-4)\) determine the coordinates and nature ...

This applet will help you in visualizing the effects of transformations on functions. Move the sliders on the right to change the translation and scaling factors ...

This paper provides another proof of the Attouch Theorem relating the epigraphical limit of sequences of convex functions to the set limit of the graphs of the subdifferentials.