A translation is a shift of the graph either horizontally parallel to the \(x\)-axis or vertically parallel to the \(y\)-axis. If \(f(x) = x^2\), then \(f(x) + a = x^2 + a\). The value of \(a\) ...

This paper presents a conceptual analysis for students' images of graphs and their extension to graphs of two-variable functions. We use the conceptual analysis, based on quantitative and ...

In the applet below is intended to help you understand the connection between the graph of a function and the function itself. Recall that a function can be thought of as a machine which takes an ...

The statistical physics of graphs and partition functions represents a vibrant intersection of graph theory, statistical mechanics and computational complexity. By summing over an ensemble of ...