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 ...

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 \(a\) ...

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 ...

A new study from Uppsala University shows that compared to non-shift workers, shift workers needed more time to complete a test that is frequently used by physicians to screen for cognitive impairment ...